{"id":1624,"date":"2021-05-19T16:45:07","date_gmt":"2021-05-19T16:45:07","guid":{"rendered":"https:\/\/pressbooks.bccampus.ca\/math53\/chapter\/integer-exponents-and-scientific-notation\/"},"modified":"2023-07-30T01:15:32","modified_gmt":"2023-07-30T01:15:32","slug":"integer-exponents-and-scientific-notation","status":"publish","type":"chapter","link":"https:\/\/pressbooks.bccampus.ca\/math53\/chapter\/integer-exponents-and-scientific-notation\/","title":{"raw":"5.3 Integer Exponents and Scientific Notation","rendered":"5.3 Integer Exponents and Scientific Notation"},"content":{"raw":"[latexpage]\r\n<div class=\"textbox textbox--learning-objectives\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">Learning Objectives<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n\r\nBy the end of this section, you will be able to:\r\n<ul>\r\n \t<li>Use the definition of a negative exponent<\/li>\r\n \t<li>Simplify expressions with integer exponents<\/li>\r\n \t<li>Convert from decimal notation to scientific notation<\/li>\r\n \t<li>Convert scientific notation to decimal form<\/li>\r\n \t<li>Multiply and divide using scientific notation<\/li>\r\n<\/ul>\r\n<\/div>\r\n<\/div>\r\n<h1>Use the Definition of a Negative Exponent<\/h1>\r\n<p id=\"fs-id1169597447461\">We saw that the Quotient Property for Exponents introduced earlier in this chapter, has two forms depending on whether the exponent is larger in the numerator or the denominator.<\/p>\r\n\r\n<div id=\"fs-id1169597539814\" data-type=\"note\">\r\n<div data-type=\"title\">\r\n<div class=\"textbox textbox--key-takeaways\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">Quotient Property for Exponents<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n<p id=\"fs-id1169597504268\">If \\(a\\) is a real number, \\(a\\ne 0\\), and \\(m\\phantom{\\rule{0.2em}{0ex}}\\text{and}\\phantom{\\rule{0.2em}{0ex}}n\\) are whole numbers, then<\/p>\r\n\r\n<div data-type=\"equation\" data-label=\"\"><img class=\"alignnone wp-image-1605\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/uploads\/sites\/1441\/2021\/05\/Screenshot-2021-02-25-at-8.19.54-AM.png\" alt=\".\" width=\"379\" height=\"49\" \/><\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<p id=\"fs-id1169597389005\">What if we just subtract exponents regardless of which is larger?<\/p>\r\n<p id=\"fs-id1169597579977\">Let\u2019s consider \\(\\frac{{x}^{2}}{{x}^{5}}\\).<\/p>\r\nWe subtract the exponent in the denominator from the exponent in the numerator.\r\n<div class=\"unnumbered\" data-type=\"equation\" data-label=\"\">\\(\\begin{array}{c}\\hfill \\frac{{x}^{2}}{{x}^{5}}\\hfill \\\\ \\hfill {x}^{2-5}\\hfill \\\\ \\hfill {x}^{-3}\\hfill \\end{array}\\)<\/div>\r\n<p id=\"fs-id1169597492100\">We can also simplify \\(\\frac{{x}^{2}}{{x}^{5}}\\) by dividing out common factors:<\/p>\r\n<span id=\"fs-id1169597389579\" data-type=\"media\" data-alt=\"Illustrated in this figure is x times x divided by x times x times x times x times x. Two xes cancel out in the numerator and denominator. Below this is the simplified term: 1 divided by x cubed.\"><img class=\"aligncenter\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/uploads\/sites\/1441\/2021\/06\/CNX_ElemAlg_Figure_06_07_001_img_new.jpg\" alt=\"Illustrated in this figure is x times x divided by x times x times x times x times x. Two xes cancel out in the numerator and denominator. Below this is the simplified term: 1 divided by x cubed.\" data-media-type=\"image\/jpeg\" \/><\/span>\r\n<p id=\"fs-id1169597357807\">This implies that \\({x}^{-3}=\\frac{1}{{x}^{3}}\\) and it leads us to the definition of a <em data-effect=\"italics\">negative exponent<\/em>.<\/p>\r\n\r\n<div id=\"fs-id1169597337099\" data-type=\"note\">\r\n<div data-type=\"title\">\r\n<div class=\"textbox textbox--key-takeaways\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">Negative Exponent<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n\r\nIf \\(n\\) is an integer and \\(a\\ne 0\\), then \\({a}^{-n}=\\frac{1}{{a}^{n}}\\).\r\n\r\n<\/div>\r\n<\/div>\r\n&nbsp;\r\n\r\n<\/div>\r\n<\/div>\r\n<p id=\"fs-id1169597576960\">The <span class=\"no-emphasis\" data-type=\"term\">negative exponent<\/span> tells us we can re-write the expression by taking the reciprocal of the base and then changing the sign of the exponent.<\/p>\r\n<p id=\"fs-id1169597478894\">Any expression that has negative exponents is not considered to be in simplest form. We will use the definition of a <span class=\"no-emphasis\" data-type=\"term\">negative exponent<\/span> and other properties of exponents to write the expression with only positive exponents.<\/p>\r\n<p id=\"fs-id1169597502645\">For example, if after simplifying an expression we end up with the expression \\({x}^{-3}\\), we will take one more step and write \\(\\frac{1}{{x}^{3}}\\). The answer is considered to be in simplest form when it has only positive exponents.<\/p>\r\n\r\n<div class=\"textbox textbox--examples\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">EXAMPLE 1<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n<div id=\"fs-id1169597358215\" data-type=\"problem\">\r\n<p id=\"fs-id1169597383767\">Simplify: a) \\({4}^{-2}\\) b) \\({10}^{-3}\\).<\/p>\r\n\r\n<\/div>\r\n<div id=\"fs-id1169597393699\" data-type=\"solution\">\r\n<div data-type=\"title\"><\/div>\r\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\r\n<table id=\"eip-426\" class=\"unnumbered unstyled\" summary=\".\">\r\n<tbody>\r\n<tr>\r\n<td>a)<\/td>\r\n<td>\\({4}^{-2}\\)<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Use the definition of a negative exponent, \\({a}^{-n}=\\frac{1}{{a}^{n}}\\).<\/td>\r\n<td>\\(\\frac{1}{{4}^{2}}\\)<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Simplify.<\/td>\r\n<td>\\(\\frac{1}{16}\\)<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>b)<\/td>\r\n<td>\\({10}^{-3}\\)<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Use the definition of a negative exponent, \\({a}^{-n}=\\frac{1}{{a}^{n}}\\).<\/td>\r\n<td>\\(\\frac{1}{{10}^{3}}\\)<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Simplify.<\/td>\r\n<td>\\(\\frac{1}{1000}\\)<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">TRY IT 1.1<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n<div id=\"fs-id1169597534816\" data-type=\"problem\">\r\n<p id=\"fs-id1169597341315\">Simplify: a) \\({2}^{-3}\\) b) \\({10}^{-7}\\).<\/p>\r\n\r\n<\/div>\r\n<div data-type=\"solution\"><details><summary>Show answer<\/summary>\r\n<p id=\"fs-id1169597541824\">a) \\(\\frac{1}{8}\\) b) \\(\\frac{1}{{10}^{7}}\\)<\/p>\r\n\r\n<\/details><\/div>\r\n<\/div>\r\n<\/div>\r\n<div id=\"fs-id1169597511869\" class=\"try\" data-type=\"note\">\r\n<div id=\"fs-id1169597441593\" data-type=\"exercise\">\r\n<div id=\"fs-id1169597534816\" data-type=\"problem\">\r\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">TRY IT 1.2<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n<div id=\"fs-id1169597351516\" data-type=\"problem\">\r\n\r\nSimplify: a) \\({3}^{-2}\\) b) \\({10}^{-4}\\).\r\n\r\n<\/div>\r\n<div id=\"fs-id1169597500356\" data-type=\"solution\"><details><summary>Show answer<\/summary>\r\n<p id=\"fs-id1169597411392\">a) \\(\\frac{1}{9}\\) b) \\(\\frac{1}{10,000}\\)<\/p>\r\n\r\n<\/details><\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<p id=\"fs-id1169597339847\">In <a class=\"autogenerated-content\" href=\"#fs-id1169597358215\">(Example 1)<\/a> we raised an integer to a negative exponent. What happens when we raise a fraction to a negative exponent? We\u2019ll start by looking at what happens to a fraction whose numerator is one and whose denominator is an integer raised to a negative exponent.<\/p>\r\n\r\n<table id=\"eip-532\" class=\"unnumbered unstyled\" summary=\".\">\r\n<tbody>\r\n<tr>\r\n<td><\/td>\r\n<td>\\(\\dfrac{1}{{a}^{-n}}\\)<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Use the definition of a negative exponent, \\({a}^{-n}=\\dfrac{1}{{a}^{n}}\\).<\/td>\r\n<td>\\(\\dfrac{1}{\\color{red}{\\frac{1}{{a}^{n}}}}\\)<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Simplify the complex fraction.<\/td>\r\n<td>\\(1\\cdot\\frac{{a}^{n}}{1}\\)<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Multiply.<\/td>\r\n<td>\\({a}^{n}\\)<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<p id=\"fs-id1169597484548\">This leads to the Property of Negative Exponents.<\/p>\r\n\r\n<div class=\"textbox textbox--key-takeaways\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">Property of Negative Exponents<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n\r\nIf \\(n\\) is an integer and \\(a\\ne 0\\), then \\(\\frac{1}{{a}^{-n}}={a}^{n}\\).\r\n\r\n<\/div>\r\n<\/div>\r\n<div id=\"fs-id1169597577846\" data-type=\"note\">\r\n<div class=\"textbox textbox--examples\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">EXAMPLE 2<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n<div id=\"fs-id1169597529407\" data-type=\"problem\">\r\n\r\nSimplify: a) \\(\\frac{1}{{y}^{-4}}\\) b) \\(\\frac{1}{{3}^{-2}}\\).\r\n\r\n<\/div>\r\n<div id=\"fs-id1169597395509\" data-type=\"solution\">\r\n<div data-type=\"title\"><\/div>\r\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\r\n<table id=\"eip-453\" class=\"unnumbered unstyled\" summary=\".\">\r\n<tbody>\r\n<tr>\r\n<td>a)<\/td>\r\n<td>\\(\\frac{1}{{y}^{-4}}\\)<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Use the property of a negative exponent, \\(\\frac{1}{{a}^{-n}}={a}^{n}\\).<\/td>\r\n<td>\\({y}^{4}\\)<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>b)<\/td>\r\n<td>\\(\\frac{1}{{3}^{-2}}\\)<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Use the property of a negative exponent, \\(\\frac{1}{{a}^{-n}}={a}^{n}\\).<\/td>\r\n<td>\\({3}^{2}\\)<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Simplify.<\/td>\r\n<td>\\(9\\)<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">TRY IT 2.1<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n<div id=\"fs-id1169597467255\" data-type=\"problem\">\r\n<p id=\"fs-id1169597527634\">Simplify: a) \\(\\frac{1}{{p}^{-8}}\\) b) \\(\\frac{1}{{4}^{-3}}\\).<\/p>\r\n\r\n<\/div>\r\n<div id=\"fs-id1169597500869\" data-type=\"solution\"><details><summary>Show answer<\/summary>\r\n<p id=\"fs-id1169597465620\">a) \\({p}^{8}\\) b) \\(64\\)<\/p>\r\n\r\n<\/details><\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<div id=\"fs-id1169597490680\" class=\"try\" data-type=\"note\">\r\n<div id=\"fs-id1169597430976\" data-type=\"exercise\">\r\n<div id=\"fs-id1169597500869\" data-type=\"solution\">\r\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">TRY IT 2.2<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n<div id=\"fs-id1169597444878\" data-type=\"problem\">\r\n<p id=\"fs-id1169597447912\">Simplify: a) \\(\\frac{1}{{q}^{-7}}\\) b) \\(\\frac{1}{{2}^{-4}}\\).<\/p>\r\n\r\n<\/div>\r\n<div id=\"fs-id1169597510009\" data-type=\"solution\"><details><summary>Show answer<\/summary>\r\n<p id=\"fs-id1169597350486\">a) \\({q}^{7}\\) b) \\(16\\)<\/p>\r\n\r\n<\/details><\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<p id=\"fs-id1169597393899\">Suppose now we have a fraction raised to a negative exponent. Let\u2019s use our definition of negative exponents to lead us to a new property.<\/p>\r\n\r\n<table id=\"eip-239\" summary=\".\">\r\n<tbody>\r\n<tr>\r\n<td><\/td>\r\n<td>\\({\\left(\\frac{3}{4}\\right)}^{-2}\\)<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Use the definition of a negative exponent, \\({a}^{-n}=\\frac{1}{{a}^{n}}\\).<\/td>\r\n<td>\\(\\frac{1}{{\\left(\\frac{3}{4}\\right)}^{2}}\\)<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Simplify the denominator.<\/td>\r\n<td>\\(\\frac{1}{\\frac{9}{16}}\\)<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Simplify the complex fraction.<\/td>\r\n<td>\\(\\frac{16}{9}\\)<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>But we know that \\(\\frac{16}{9}\\) is \\({\\left(\\frac{4}{3}\\right)}^{2}\\).<\/td>\r\n<td><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>This tells us that:<\/td>\r\n<td>\\({\\left(\\frac{3}{4}\\right)}^{-2}={\\left(\\frac{4}{3}\\right)}^{2}\\)<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<p id=\"fs-id1169597409988\">To get from the original fraction raised to a negative exponent to the final result, we took the reciprocal of the base\u2014the fraction\u2014and changed the sign of the exponent.<\/p>\r\n<p id=\"fs-id1169597515519\">This leads us to the <em data-effect=\"italics\">Quotient to a Negative Power Property<\/em>.<\/p>\r\n\r\n<div class=\"textbox textbox--key-takeaways\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">Quotient to a Negative Exponent Property<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n\r\nIf \\(a\\phantom{\\rule{0.2em}{0ex}}\\text{and}\\phantom{\\rule{0.2em}{0ex}}b\\) are real numbers, \\(a\\ne 0,b\\ne 0\\), and \\(n\\) is an integer, then \\({\\left(\\frac{a}{b}\\right)}^{-n}={\\left(\\frac{b}{a}\\right)}^{n}\\).\r\n\r\n<\/div>\r\n<\/div>\r\n<div id=\"fs-id1169597416290\" data-type=\"note\">\r\n<div class=\"textbox textbox--examples\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">EXAMPLE 3<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n<div id=\"fs-id1169597577456\" data-type=\"problem\">\r\n<p id=\"fs-id1169597492476\">Simplify: a) \\({\\left(\\frac{5}{7}\\right)}^{-2}\\) b) \\({\\left(-\\frac{2x}{y}\\right)}^{-3}\\).<\/p>\r\n\r\n<\/div>\r\n<div id=\"fs-id1169597580588\" data-type=\"solution\">\r\n<div data-type=\"title\"><\/div>\r\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\r\n<table id=\"eip-116\" class=\"unnumbered unstyled\" summary=\".\">\r\n<tbody>\r\n<tr>\r\n<td>a)<\/td>\r\n<td>\\({\\left(\\frac{5}{7}\\right)}^{-2}\\)<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Use the Quotient to a Negative Exponent Property, \\({\\left(\\frac{a}{b}\\right)}^{-n}={\\left(\\frac{b}{a}\\right)}^{n}\\).<\/td>\r\n<td><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Take the reciprocal of the fraction and change the sign of the exponent.<\/td>\r\n<td>\\({\\left(\\frac{7}{5}\\right)}^{2}\\)<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Simplify.<\/td>\r\n<td>\\(\\frac{49}{25}\\)<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>b)<\/td>\r\n<td>\\({\\left(-\\frac{2x}{y}\\right)}^{-3}\\)<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Use the Quotient to a Negative Exponent Property, \\({\\left(\\frac{a}{b}\\right)}^{-n}={\\left(\\frac{b}{a}\\right)}^{n}\\).<\/td>\r\n<td><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Take the reciprocal of the fraction and change the sign of the exponent.<\/td>\r\n<td>\\({\\left(-\\frac{y}{2x}\\right)}^{3}\\)<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Simplify.<\/td>\r\n<td>\\(-\\frac{{y}^{3}}{8{x}^{3}}\\)<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">TRY IT 3.1<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n<div id=\"fs-id1169597520921\" data-type=\"problem\">\r\n<p id=\"fs-id1169597467530\">Simplify: a) \\({\\left(\\frac{2}{3}\\right)}^{-4}\\) b) \\({\\left(-\\frac{6m}{n}\\right)}^{-2}\\).<\/p>\r\n\r\n<\/div>\r\n<div id=\"fs-id1169597540982\" data-type=\"solution\"><details><summary>Show answer<\/summary>\r\n<p id=\"fs-id1169597507465\">a) \\(\\frac{81}{16}\\) b) \\(\\frac{{n}^{2}}{36{m}^{2}}\\)<\/p>\r\n\r\n<\/details><\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<div id=\"fs-id1169597422172\" class=\"try\" data-type=\"note\">\r\n<div id=\"fs-id1169597533646\" data-type=\"exercise\">\r\n<div id=\"fs-id1169597540982\" data-type=\"solution\">\r\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">TRY IT 3.2<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n<div data-type=\"problem\">\r\n<p id=\"fs-id1169597702065\">Simplify: a) \\({\\left(\\frac{3}{5}\\right)}^{-3}\\) b) \\({\\left(-\\frac{a}{2b}\\right)}^{-4}\\).<\/p>\r\n\r\n<\/div>\r\n<div id=\"fs-id1169597415785\" data-type=\"solution\"><details><summary>Show answer<\/summary>\r\n<p id=\"fs-id1169597500693\">a) \\(\\frac{125}{27}\\) b) \\(\\frac{16{b}^{4}}{{a}^{4}}\\)<\/p>\r\n\r\n<\/details><\/div>\r\n<\/div>\r\n<\/div>\r\nWhen simplifying an expression with exponents, we must be careful to correctly identify the base.\r\n\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<div class=\"textbox textbox--examples\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">EXAMPLE 4<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n<div id=\"fs-id1169597540378\" data-type=\"problem\">\r\n<p id=\"fs-id1169597703489\">Simplify: a) \\({\\left(-3\\right)}^{-2}\\) b) \\(-{3}^{-2}\\) c) \\({\\left(-\\frac{1}{3}\\right)}^{-2}\\) d) \\(-{\\left(\\frac{1}{3}\\right)}^{-2}\\).<\/p>\r\n\r\n<\/div>\r\n<div id=\"fs-id1169597467914\" data-type=\"solution\">\r\n<div data-type=\"title\"><\/div>\r\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\r\n<table id=\"eip-407\" class=\"unnumbered unstyled\" summary=\".\">\r\n<tbody>\r\n<tr>\r\n<td>a) Here the exponent applies to the base \\(-3\\).<\/td>\r\n<td>\\({\\left(-3\\right)}^{-2}\\)<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Take the reciprocal of the base and change the sign of the exponent.<\/td>\r\n<td>\\(\\frac{1}{{\\left(-3\\right)}^{2}}\\)<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Simplify.<\/td>\r\n<td>\\(\\frac{1}{9}\\)<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>b) The expression \\(-{3}^{-2}\\) means \"find the opposite of \\({3}^{-2}\\).\" Here the exponent applies to the base \\({\\left(-\\frac{1}{3}\\right)}^{}\\).<\/td>\r\n<td>\\(-{3}^{-2}\\)<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Rewrite as a product with \\(-1\\).<\/td>\r\n<td>\\(-1\\cdot{3}^{-2}\\)<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Take the reciprocal of the base and change the sign of the exponent.<\/td>\r\n<td>\\(-1\\cdot\\frac{1}{{3}^{2}}\\)<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Simplify.<\/td>\r\n<td>\\(-\\frac{1}{9}\\)<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>c) Here the exponent applies to the base \\({\\left(-\\frac{1}{3}\\right)}^{}\\).<\/td>\r\n<td>\\({\\left(-\\frac{1}{3}\\right)}^{-2}\\)<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Take the reciprocal of the base and change the sign of the exponent.<\/td>\r\n<td>\\({\\left(-\\frac{3}{1}\\right)}^{2}\\)<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Simplify.<\/td>\r\n<td>\\(9\\)<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>d) The expression \\(-{\\left(\\frac{1}{3}\\right)}^{-2}\\) means \"find the opposite of \\({\\left(\\frac{1}{3}\\right)}^{-2}\\).\" Here the exponent applies to the base \\(\\left(\\frac{1}{3}\\right)\\).<\/td>\r\n<td>\\(\\)<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Rewrite as a product with \\(-1\\).<\/td>\r\n<td>\\(-1\\cdot{\\left(\\frac{1}{3}\\right)}^{-2}\\)<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Take the reciprocal of the base and change the sign of the exponent.<\/td>\r\n<td>\\(-1\\cdot{\\left(\\frac{3}{1}\\right)}^{2}\\)<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Simplify.<\/td>\r\n<td>\\(-9\\)<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">TRY IT 4.1<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n<div id=\"fs-id1169597457044\" data-type=\"problem\">\r\n<p id=\"fs-id1169597457046\">Simplify: a) \\({\\left(-5\\right)}^{-2}\\) b) \\(-{5}^{-2}\\) c) \\({\\left(-\\frac{1}{5}\\right)}^{-2}\\) d) \\(-{\\left(\\frac{1}{5}\\right)}^{-2}\\).<\/p>\r\n\r\n<\/div>\r\n<div id=\"fs-id1169597577197\" data-type=\"solution\"><details><summary>Show answer<\/summary>\r\n<p id=\"fs-id1169597577199\">a) \\(\\frac{1}{25}\\) b) \\(-\\frac{1}{25}\\) c) 25 d) \\(-25\\)<\/p>\r\n\r\n<\/details><\/div>\r\n<\/div>\r\n<\/div>\r\n<div id=\"fs-id1169597741466\" class=\"try\" data-type=\"note\">\r\n<div id=\"fs-id1169597741469\" data-type=\"exercise\">\r\n<div id=\"fs-id1169597577197\" data-type=\"solution\">\r\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">TRY IT 4.2<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n<div id=\"fs-id1169597540994\" data-type=\"problem\">\r\n<p id=\"fs-id1169597540997\">Simplify: a) \\({\\left(-7\\right)}^{-2}\\) b) \\(-{7}^{-2}\\), c) \\({\\left(-\\frac{1}{7}\\right)}^{-2}\\) d) \\(-{\\left(\\frac{1}{7}\\right)}^{-2}\\).<\/p>\r\n\r\n<\/div>\r\n<div data-type=\"solution\"><details><summary>Show answer<\/summary>\r\n<p id=\"fs-id1169597483796\">a) \\(\\frac{1}{49}\\) b) \\(-\\frac{1}{49}\\) c) 49 d) \\(-49\\)<\/p>\r\n\r\n<\/details><\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<p id=\"fs-id1169597533353\">We must be careful to follow the Order of Operations. In the next example, parts (a) and (b) look similar, but the results are different.<\/p>\r\n\r\n<div class=\"textbox textbox--examples\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">EXAMPLE 5<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n<div id=\"fs-id1169597492583\" data-type=\"problem\">\r\n<p id=\"fs-id1169597492586\">Simplify: a) \\(4\\cdot{2}^{-1}\\) b) \\({\\left(4\\cdot 2\\right)}^{-1}\\).<\/p>\r\n\r\n<\/div>\r\n<div id=\"fs-id1169597684591\" data-type=\"solution\">\r\n<div data-type=\"title\"><\/div>\r\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\r\n<table id=\"eip-779\" class=\"unnumbered unstyled\" summary=\"\/\">\r\n<tbody>\r\n<tr>\r\n<td>a)\r\nDo exponents before multiplication.<\/td>\r\n<td>\\(4\\cdot{2}^{-1}\\)<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Use \\({a}^{-n}=\\frac{1}{{a}^{n}}\\).<\/td>\r\n<td>\\(4\\cdot\\frac{1}{{2}^{1}}\\)<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Simplify.<\/td>\r\n<td>\\(2\\)<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>b)<\/td>\r\n<td>\\({\\left(4\\cdot 2\\right)}^{-1}\\)<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Simplify inside the parentheses first.<\/td>\r\n<td>\\({\\left(8\\right)}^{-1}\\)<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Use \\({a}^{-n}=\\frac{1}{{a}^{n}}\\).<\/td>\r\n<td>\\(\\frac{1}{{8}^{1}}\\)<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Simplify.<\/td>\r\n<td>\\(\\frac{1}{8}\\)<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">TRY IT 5.1<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n<div id=\"fs-id1169597479266\" data-type=\"problem\">\r\n<p id=\"fs-id1169597689696\">Simplify: a) \\(6\\cdot{3}^{-1}\\) \u00a0\u00a0 b) \\({\\left(6\\cdot3\\right)}^{-1}\\).<\/p>\r\n\r\n<\/div>\r\n<div id=\"fs-id1169597576993\" data-type=\"solution\"><details><summary>Show answer<\/summary>\r\n<p id=\"fs-id1169597576996\">a) \\(2\\) \u00a0\u00a0 b) \\(\\frac{1}{18}\\)<\/p>\r\n\r\n<\/details><\/div>\r\n<\/div>\r\n<\/div>\r\n<div id=\"fs-id1169597479261\" class=\"try\" data-type=\"note\">\r\n<div data-type=\"exercise\">\r\n<div id=\"fs-id1169597576993\" data-type=\"solution\">\r\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">TRY IT 5.2<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n<div id=\"fs-id1169597577016\" data-type=\"problem\">\r\n<p id=\"fs-id1169597577018\">Simplify: a) \\(8\\cdot{2}^{-2}\\) \u00a0\u00a0 b) \\({\\left(8\\cdot 2\\right)}^{-2}\\).<\/p>\r\n\r\n<\/div>\r\n<div data-type=\"solution\"><details><summary>Show answer<\/summary>\r\n<p id=\"fs-id1169597533015\">a) 2 \u00a0\u00a0 b) \\(\\frac{1}{256}\\)<\/p>\r\n\r\n<\/details><\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<p id=\"fs-id1169597689365\">When a variable is raised to a negative exponent, we apply the definition the same way we did with numbers. We will assume all variables are non-zero.<\/p>\r\n\r\n<div class=\"textbox textbox--examples\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">EXAMPLE 6<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n<div id=\"fs-id1169597479240\" data-type=\"problem\">\r\n<p id=\"fs-id1169597479242\">Simplify: a) \\({x}^{-6}\\) \u00a0\u00a0 b) \\({\\left({u}^{4}\\right)}^{-3}\\).<\/p>\r\n\r\n<\/div>\r\n<div id=\"fs-id1169597688171\" data-type=\"solution\">\r\n<div data-type=\"title\"><\/div>\r\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\r\n<div data-type=\"title\">\r\n<table style=\"border-collapse: collapse;width: 100%\" border=\"0\">\r\n<tbody>\r\n<tr>\r\n<td style=\"width: 50%\">a)<\/td>\r\n<td style=\"width: 50%\">\\({x}^{-6}\\)<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 50%\">Use the definition of a negative exponent \\({a}^{-n}=\\frac{1}{{a}^{n}}\\)<\/td>\r\n<td style=\"width: 50%\">\\(\\frac{1}{{x}^{6}}\\)<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 50%\">b)<\/td>\r\n<td style=\"width: 50%\">\\({\\left({u}^{4}\\right)}^{-3}\\)<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 50%\">Use the definition of a negative exponent \\({a}^{-n}=\\frac{1}{{a}^{n}}\\).<\/td>\r\n<td style=\"width: 50%\">\\(\\frac{1}{{\\left({u}^{4}\\right)}^{3}}\\)<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 50%\">Simplify.<\/td>\r\n<td style=\"width: 50%\">\\(\\frac{1}{{u}^{12}}\\)<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">TRY IT 6.1<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n<div id=\"fs-id1169597478468\" data-type=\"problem\">\r\n<p id=\"fs-id1169597541016\">Simplify: a) \\({y}^{-7}\\) \u00a0\u00a0 b) \\({\\left({z}^{3}\\right)}^{-5}\\)<\/p>\r\n\r\n<\/div>\r\n<div id=\"fs-id1169597378928\" data-type=\"solution\"><details><summary>Show answer<\/summary>\r\n<p id=\"fs-id1169597479516\">a) \\(\\frac{1}{{y}^{7}}\\) \u00a0\u00a0 b) \\(\\frac{1}{{z}^{15}}\\)<\/p>\r\n\r\n<\/details><\/div>\r\n<\/div>\r\n<\/div>\r\n<div id=\"fs-id1169597478463\" class=\"try\" data-type=\"note\">\r\n<div id=\"fs-id1169597478466\" data-type=\"exercise\">\r\n<div id=\"fs-id1169597478468\" data-type=\"problem\">\r\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">TRY IT 6.2<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n<div id=\"fs-id1169597507834\" data-type=\"problem\">\r\n<p id=\"fs-id1169597507836\">Simplify: a) \\({p}^{-9}\\) \u00a0\u00a0 b) \\({\\left({q}^{4}\\right)}^{-6}\\).<\/p>\r\n\r\n<\/div>\r\n<div id=\"fs-id1169597689772\" data-type=\"solution\"><details><summary>Show answer<\/summary>\r\n<p id=\"fs-id1169597689774\">a) \\(\\frac{1}{{p}^{9}}\\) \u00a0\u00a0 b) \\(\\frac{1}{{q}^{24}}\\)<\/p>\r\n\r\n<\/details><\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<p id=\"fs-id1169597539260\">When there is a product and an exponent we have to be careful to apply the exponent to the correct quantity. According to the Order of Operations, we simplify expressions in parentheses before applying exponents. We\u2019ll see how this works in the next example.<\/p>\r\n\r\n<div class=\"textbox textbox--examples\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">EXAMPLE 7<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n<div id=\"fs-id1169597688873\" data-type=\"problem\">\r\n<p id=\"fs-id1169597688875\">Simplify: a) \\(5{y}^{-1}\\) \u00a0\u00a0 b) \\({\\left(5y\\right)}^{-1}\\) c) \\({\\left(-5y\\right)}^{-1}\\).<\/p>\r\n\r\n<\/div>\r\n<div id=\"fs-id1169597690063\" data-type=\"solution\">\r\n<div data-type=\"title\"><\/div>\r\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\r\n<div data-type=\"title\">\r\n<table style=\"border-collapse: collapse;width: 100%;height: 140px\" border=\"0\">\r\n<tbody>\r\n<tr style=\"height: 14px\">\r\n<td style=\"width: 50%;height: 14px\">a) Notice the exponent applies to just the base.<\/td>\r\n<td style=\"width: 50%;height: 14px\">\\(5{y}^{-1}\\)<\/td>\r\n<\/tr>\r\n<tr style=\"height: 14px\">\r\n<td style=\"width: 50%;height: 14px\">Take the reciprocal of \\(y\\) and change the sign of the exponent.<\/td>\r\n<td style=\"width: 50%;height: 14px\">\\(5\\cdot\\frac{1}{{y}^{1}}\\)<\/td>\r\n<\/tr>\r\n<tr style=\"height: 14px\">\r\n<td style=\"width: 50%;height: 14px\">Simplify.<\/td>\r\n<td style=\"width: 50%;height: 14px\">\\(\\frac{5}{y}\\)<\/td>\r\n<\/tr>\r\n<tr style=\"height: 14px\">\r\n<td style=\"width: 50%;height: 14px\">b) Here the parentheses make the exponent apply to the base.<\/td>\r\n<td style=\"width: 50%;height: 14px\">\\({\\left(5y\\right)}^{-1}\\)<\/td>\r\n<\/tr>\r\n<tr style=\"height: 14px\">\r\n<td style=\"width: 50%;height: 14px\">Take the reciprocal of \\(5y\\) and change the sign of the exponent.<\/td>\r\n<td style=\"width: 50%;height: 14px\">\\(\\frac{1}{{\\left(5y\\right)}^{1}}\\)<\/td>\r\n<\/tr>\r\n<tr style=\"height: 14px\">\r\n<td style=\"width: 50%;height: 14px\">Simplify.<\/td>\r\n<td style=\"width: 50%;height: 14px\">\\(\\frac{1}{5y}\\)<\/td>\r\n<\/tr>\r\n<tr style=\"height: 14px\">\r\n<td style=\"width: 50%;height: 14px\">c) The base here is \\(-5y\\).<\/td>\r\n<td style=\"width: 50%;height: 14px\">\\({\\left(-5y\\right)}^{-1}\\)<\/td>\r\n<\/tr>\r\n<tr style=\"height: 14px\">\r\n<td style=\"width: 50%;height: 14px\">Take the reciprocal of \\(-5y\\) and change the sign of the exponent.<\/td>\r\n<td style=\"width: 50%;height: 14px\">\\(\\frac{1}{{\\left(-5y\\right)}^{1}}\\)<\/td>\r\n<\/tr>\r\n<tr style=\"height: 14px\">\r\n<td style=\"width: 50%;height: 14px\">Simplify.<\/td>\r\n<td style=\"width: 50%;height: 14px\">\\(\\frac{1}{-5y}\\)<\/td>\r\n<\/tr>\r\n<tr style=\"height: 14px\">\r\n<td style=\"width: 50%;height: 14px\">Use \\(\\frac{a}{-b}=-\\frac{a}{b}\\)<\/td>\r\n<td style=\"width: 50%;height: 14px\">\\(-\\frac{1}{5y}\\)<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">TRY IT 7.1<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n<div id=\"fs-id1169597691040\" data-type=\"problem\">\r\n<p id=\"fs-id1169597691042\">Simplify: a) \\(8{p}^{-1}\\) b) \\({\\left(8p\\right)}^{-1}\\) c) \\({\\left(-8p\\right)}^{-1}\\).<\/p>\r\n\r\n<\/div>\r\n<div id=\"fs-id1169597539540\" data-type=\"solution\"><details><summary>Show answer<\/summary>\r\n<p id=\"fs-id1169597539542\">a) \\(\\frac{8}{p}\\) b) \\(\\frac{1}{8p}\\) c) \\(-\\frac{1}{8p}\\)<\/p>\r\n\r\n<\/details><\/div>\r\n<\/div>\r\n<\/div>\r\n<div id=\"fs-id1169597691035\" class=\"try\" data-type=\"note\">\r\n<div id=\"fs-id1169597691038\" data-type=\"exercise\">\r\n<div id=\"fs-id1169597691040\" data-type=\"problem\">\r\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">TRY IT 7.2<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n<div data-type=\"problem\">\r\n\r\nSimplify: a) \\({11q}^{-1}\\)\u00a0 \u00a0b) \\({\\left(11q\\right)}^{-1}\\)\u00a0 c) \\({\\left(-11q\\right)}^{-1}\\).\r\n\r\n<\/div>\r\n<div id=\"fs-id1169597738793\" data-type=\"solution\"><details><summary>Show answer<\/summary>\r\n<p id=\"fs-id1169597738795\">a) \\(\\frac{11}{q}\\)\u00a0 \u00a0b) \\(\\frac{1}{11q}\\)\u00a0 \u00a0c) \\(-\\frac{1}{11q}\\)<\/p>\r\n\r\n<\/details><\/div>\r\n<\/div>\r\n<\/div>\r\nWith negative exponents, the Quotient Rule needs only one form \\(\\frac{{a}^{m}}{{a}^{n}}={a}^{m-n}\\), for \\(a\\ne 0\\). When the exponent in the denominator is larger than the exponent in the numerator, the exponent of the quotient will be negative.\r\n\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<h1>Simplify Expressions with Integer Exponents<\/h1>\r\n<p id=\"fs-id1169597539593\">All of the exponent properties we developed earlier in the chapter with whole number exponents apply to integer exponents, too. We restate them here for reference.<\/p>\r\n\r\n<div id=\"fs-id1169597539598\" data-type=\"note\">\r\n<div data-type=\"title\">\r\n<div class=\"textbox textbox--key-takeaways\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">Summary of Exponent Properties<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n<p id=\"fs-id1169597688590\">If \\(a\\phantom{\\rule{0.2em}{0ex}}\\text{and}\\phantom{\\rule{0.2em}{0ex}}b\\) are real numbers, and \\(m\\phantom{\\rule{0.2em}{0ex}}\\text{and}\\phantom{\\rule{0.2em}{0ex}}n\\) are integers, then<\/p>\r\n\r\n<div class=\"unnumbered\" data-type=\"equation\" data-label=\"\">\\(\\begin{array}{cccccc}\\mathbf{\\text{Product Property}}\\hfill &amp; &amp; &amp; \\hfill {a}^{m}\\cdot{a}^{n}&amp; =\\hfill &amp; {a}^{m+n}\\hfill \\\\ \\mathbf{\\text{Power Property}}\\hfill &amp; &amp; &amp; \\hfill {\\left({a}^{m}\\right)}^{n}&amp; =\\hfill &amp; {a}^{m\\cdot n}\\hfill \\\\ \\mathbf{\\text{Product to a Power}}\\hfill &amp; &amp; &amp; \\hfill {\\left(ab\\right)}^{m}&amp; =\\hfill &amp; {a}^{m}{b}^{m}\\hfill \\\\ \\mathbf{\\text{Quotient Property}}\\hfill &amp; &amp; &amp; \\hfill \\frac{{a}^{m}}{{a}^{n}}&amp; =\\hfill &amp; {a}^{m-n},a\\ne 0\\hfill \\\\ \\mathbf{\\text{Zero Exponent Property}}\\hfill &amp; &amp; &amp; \\hfill {a}^{0}&amp; =\\hfill &amp; 1,a\\ne 0\\hfill \\\\ \\mathbf{\\text{Quotient to a Power Property}}\\hfill &amp; &amp; &amp; \\hfill {\\left(\\frac{a}{b}\\right)}^{m}&amp; =\\hfill &amp; \\frac{{a}^{m}}{{b}^{m}},\\phantom{\\rule{0.2em}{0ex}}\\text{}\\phantom{\\rule{0.2em}{0ex}}b\\ne 0\\hfill \\\\ \\mathbf{\\text{Properties of Negative Exponents}}\\hfill &amp; &amp; &amp; \\hfill {a}^{-n}&amp; =\\hfill &amp; \\frac{1}{{a}^{n}}\\phantom{\\rule{0.5em}{0ex}}\\text{and}\\phantom{\\rule{0.5em}{0ex}}\\frac{1}{{a}^{-n}}={a}^{n}\\hfill \\\\ \\mathbf{\\text{Quotient to a Negative Exponent}}\\hfill &amp; &amp; &amp; \\hfill {\\left(\\frac{a}{b}\\right)}^{-n}&amp; =\\hfill &amp; {\\left(\\frac{b}{a}\\right)}^{n}\\hfill \\end{array}\\)<\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<div class=\"unnumbered\" data-type=\"equation\" data-label=\"\">\r\n<div class=\"textbox textbox--examples\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">EXAMPLE 8<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n<div id=\"fs-id1169597741131\" data-type=\"problem\">\r\n<p id=\"fs-id1169597741133\">Simplify: a) \\({x}^{-4}\\cdot{x}^{6}\\) b) \\({y}^{-6}\\cdot{y}^{4}\\) c) \\({z}^{-5}\\cdot{z}^{-3}\\).<\/p>\r\n\r\n<\/div>\r\n<div id=\"fs-id1169597508211\" data-type=\"solution\">\r\n<div data-type=\"title\"><\/div>\r\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\r\n<div data-type=\"title\"><\/div>\r\n<ol id=\"fs-id1168746443625\" class=\"circled\" type=\"a\">\r\n \t<li>\r\n<table style=\"border-collapse: collapse;width: 100%;height: 42px\" border=\"0\">\r\n<tbody>\r\n<tr style=\"height: 14px\">\r\n<td style=\"width: 50%;height: 14px\"><\/td>\r\n<td style=\"width: 50%;height: 14px\">\\({x}^{-4}\\cdot{x}^{6}\\)<\/td>\r\n<\/tr>\r\n<tr style=\"height: 14px\">\r\n<td style=\"width: 50%;height: 14px\">Use the Product Property, \\({a}^{m}\\cdot{a}^{n}={a}^{m+n}\\).<\/td>\r\n<td style=\"width: 50%;height: 14px\">\\({x}^{-4+6}\\)<\/td>\r\n<\/tr>\r\n<tr style=\"height: 14px\">\r\n<td style=\"width: 50%;height: 14px\">Simplify<\/td>\r\n<td style=\"width: 50%;height: 14px\">\\({x}^{2}\\)<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<\/li>\r\n \t<li>\r\n<table style=\"border-collapse: collapse;width: 100%\" border=\"0\">\r\n<tbody>\r\n<tr>\r\n<td style=\"width: 50%\"><\/td>\r\n<td style=\"width: 50%\">\\({y}^{-6}\\cdot{y}^{4}\\)<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 50%\">Notice the same bases, so add the exponents.<\/td>\r\n<td style=\"width: 50%\">\\({y}^{-6+4}\\)<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 50%\">Simplify.<\/td>\r\n<td style=\"width: 50%\">\\({y}^{-2}\\)<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 50%\">Use the definition of a negative exponent, \\(\\frac{1}{{a}^{n}}\\).<\/td>\r\n<td style=\"width: 50%\">\\(\\frac{1}{{y}^{2}}\\)<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<\/li>\r\n \t<li>\r\n<table style=\"border-collapse: collapse;width: 100%\" border=\"0\">\r\n<tbody>\r\n<tr>\r\n<td style=\"width: 50%\"><\/td>\r\n<td style=\"width: 50%\">\\({z}^{-5}\\cdot{z}^{-3}\\)<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 50%\">Add the exponents, since the bases are the same.<\/td>\r\n<td style=\"width: 50%\">\\({z}^{-5-3}\\)<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 50%\">Simplify.<\/td>\r\n<td style=\"width: 50%\">\\({z}^{-8}\\)<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 50%\">Take the reciprocal and change the sign of the exponent, using the definition of a negative exponent.<\/td>\r\n<td style=\"width: 50%\">\\(\\frac{1}{{z}^{8}}\\)<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<\/li>\r\n<\/ol>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">TRY IT 8.1<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n<div id=\"fs-id1169597395207\" data-type=\"problem\">\r\n<p id=\"fs-id1169597395209\">Simplify: a) \\({x}^{-3}\\cdot{x}^{7}\\) b) \\({y}^{-7}\\cdot{y}^{2}\\) c) \\({z}^{-4}\\cdot{z}^{-5}\\).<\/p>\r\n\r\n<\/div>\r\n<div id=\"fs-id1169597537212\" data-type=\"solution\"><details><summary>Show answer<\/summary>\r\n<p id=\"fs-id1169597537214\">a) \\({x}^{4}\\) b) \\(\\frac{1}{{y}^{5}}\\) c) \\(\\frac{1}{{z}^{9}}\\)<\/p>\r\n\r\n<\/details><\/div>\r\n<\/div>\r\n<\/div>\r\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">TRY IT 8.2<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n<div id=\"fs-id1169597688417\" data-type=\"problem\">\r\n<p id=\"fs-id1169597688420\">Simplify: a) \\({a}^{-1}\\cdot{a}^{6}\\) b) \\({b}^{-8}\\cdot{b}^{4}\\) c) \\({c}^{-8}\\cdot{c}^{-7}\\).<\/p>\r\n\r\n<\/div>\r\n<div data-type=\"solution\"><details><summary>Show answer<\/summary>a) \\({a}^{5}\\) b) \\(\\frac{1}{{b}^{4}}\\) c) \\(\\frac{1}{{c}^{15}}\\)\r\n\r\n<\/details><\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<p id=\"fs-id1169597507987\">In the next two examples, we\u2019ll start by using the Commutative Property to group the same variables together. This makes it easier to identify the like bases before using the Product Property.<\/p>\r\n\r\n<div class=\"textbox textbox--examples\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">EXAMPLE 9<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n<div id=\"fs-id1169597687992\" data-type=\"problem\">\r\n<p id=\"fs-id1169597687994\">Simplify: \\(\\left({m}^{4}{n}^{-3}\\right)\\left({m}^{-5}{n}^{-2}\\right)\\).<\/p>\r\n\r\n<\/div>\r\n<div id=\"fs-id1169597479130\" data-type=\"solution\">\r\n<div data-type=\"title\"><\/div>\r\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\r\n<div data-type=\"title\">\r\n<table style=\"border-collapse: collapse;width: 100%\" border=\"0\">\r\n<tbody>\r\n<tr>\r\n<td style=\"width: 50%\"><\/td>\r\n<td style=\"width: 50%\">\\(\\left({m}^{4}{n}^{-3}\\right)\\left({m}^{-5}{n}^{-2}\\right)\\)<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 50%\">Use the Commutative Property to get like bases together.<\/td>\r\n<td style=\"width: 50%\">\\({m}^{4}{m}^{-5}\\cdot{n}^{-2}{n}^{-3}\\)<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 50%\">Add the exponents for each base.<\/td>\r\n<td style=\"width: 50%\">\\({m}^{-1}\\cdot{n}^{-5}\\)<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 50%\">Take the reciprocals and change the signs of the exponents.<\/td>\r\n<td style=\"width: 50%\">\\(\\frac{1}{{m}^{1}}\\cdot\\frac{1}{{n}^{5}}\\)<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 50%\">Simplify.<\/td>\r\n<td style=\"width: 50%\">\\(\\frac{1}{m{n}^{5}}\\)<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">TRY IT 9.1<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n<div data-type=\"problem\">\r\n\r\nSimplify: \\(\\left({p}^{6}{q}^{-2}\\right)\\left({p}^{-9}{q}^{-1}\\right)\\).\r\n\r\n<\/div>\r\n<div data-type=\"solution\"><details><summary>Show answer<\/summary>\\(\\frac{1}{{p}^{3}{q}^{3}}\\)\r\n\r\n<\/details><\/div>\r\n<\/div>\r\n<\/div>\r\n<div id=\"fs-id1169597689068\" class=\"try\" data-type=\"note\">\r\n<div data-type=\"exercise\">\r\n<div data-type=\"solution\">\r\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">TRY IT 9.2<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n<div id=\"fs-id1169597461048\" data-type=\"problem\">\r\n<p id=\"fs-id1169597461050\">Simplify: \\(\\left({r}^{5}{s}^{-3}\\right)\\left({r}^{-7}{s}^{-5}\\right)\\).<\/p>\r\n\r\n<\/div>\r\n<div id=\"fs-id1169597700111\" data-type=\"solution\"><details><summary>Show answer<\/summary>\r\n<p id=\"fs-id1169597700113\">\\(\\frac{1}{{r}^{2}{s}^{8}}\\)<\/p>\r\n\r\n<\/details><\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<p id=\"fs-id1169597479193\">If the monomials have numerical coefficients, we multiply the coefficients, just like we did earlier.<\/p>\r\n\r\n<div class=\"textbox textbox--examples\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">EXAMPLE 10<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n<div id=\"fs-id1169597479200\" data-type=\"problem\">\r\n<p id=\"fs-id1169597479202\">Simplify: \\(\\left(2{x}^{-6}{y}^{8}\\right)\\left(-5{x}^{5}{y}^{-3}\\right)\\).<\/p>\r\n\r\n<\/div>\r\n<div id=\"fs-id1169597479466\" data-type=\"solution\">\r\n<div data-type=\"title\"><\/div>\r\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\r\n<div data-type=\"title\">\r\n<table style=\"border-collapse: collapse;width: 100%\" border=\"0\">\r\n<tbody>\r\n<tr>\r\n<td style=\"width: 50%\"><\/td>\r\n<td style=\"width: 50%\">\\(\\left(2{x}^{-6}{y}^{8}\\right)\\left(-5{x}^{5}{y}^{-3}\\right)\\)<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 50%\">Rewrite with the like bases together.<\/td>\r\n<td style=\"width: 50%\">\\(2\\left(-5\\right)\\cdot\\left({x}^{-6}{x}^{5}\\right)\\cdot\\left({y}^{8}{y}^{-3}\\right)\\)<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 50%\">Multiply the coefficients and add the exponents of each variable.<\/td>\r\n<td style=\"width: 50%\">\\(-10\\cdot{x}^{-1}\\cdot{y}^{5}\\)<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 50%\">Use the definition of a negative exponent, \\({a}^{-n}=\\frac{1}{{a}^{n}}\\).<\/td>\r\n<td style=\"width: 50%\">\\(-10\\cdot\\frac{1}{{x}^{1}}\\cdot{y}^{5}\\)<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 50%\">Simplify.<\/td>\r\n<td style=\"width: 50%\">\\(\\frac{-10{y}^{5}}{x}\\)<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">TRY IT 10.1<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n<div id=\"fs-id1169597705546\" data-type=\"problem\">\r\n<p id=\"fs-id1169597705548\">Simplify: \\(\\left(3{u}^{-5}{v}^{7}\\right)\\left(-4{u}^{4}{v}^{-2}\\right)\\).<\/p>\r\n\r\n<\/div>\r\n<div id=\"fs-id1169597537162\" data-type=\"solution\"><details><summary>Show answer<\/summary>\r\n<p id=\"fs-id1169597537164\">\\(-\\frac{12{v}^{5}}{u}\\)<\/p>\r\n\r\n<\/details><\/div>\r\n<\/div>\r\n<\/div>\r\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">TRY IT 10.2<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n<div id=\"fs-id1169597742137\" data-type=\"problem\">\r\n<p id=\"fs-id1169597742139\">Simplify: \\(\\left(-6{c}^{-6}{d}^{4}\\right)\\left(-5{c}^{-2}{d}^{-1}\\right)\\).<\/p>\r\n\r\n<\/div>\r\n<div id=\"fs-id1169597743028\" data-type=\"solution\"><details><summary>Show answer<\/summary>\r\n<p id=\"fs-id1169597743031\">\\(\\frac{30{d}^{3}}{{c}^{8}}\\)<\/p>\r\n\r\n<\/details><\/div>\r\n<\/div>\r\n<\/div>\r\n<p id=\"fs-id1169597688547\">In the next two examples, we\u2019ll use the Power Property and the Product to a Power Property.<\/p>\r\n\r\n<div class=\"textbox textbox--examples\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">EXAMPLE 11<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n<div id=\"fs-id1169597688557\" data-type=\"problem\">\r\n<p id=\"fs-id1169597688559\">Simplify: \\({\\left(6{k}^{3}\\right)}^{-2}\\).<\/p>\r\n\r\n<\/div>\r\n<div id=\"fs-id1169597540810\" data-type=\"solution\">\r\n<div data-type=\"title\"><\/div>\r\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\r\n<div data-type=\"title\">\r\n<table style=\"border-collapse: collapse;width: 100%\" border=\"0\">\r\n<tbody>\r\n<tr>\r\n<td style=\"width: 50%\"><\/td>\r\n<td style=\"width: 50%\">\\({\\left(6{k}^{3}\\right)}^{-2}\\)<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 50%\">Use the product to a Power Property, \\({\\left(ab\\right)}^{m}={a}^{m}{b}^{m}\\).<\/td>\r\n<td style=\"width: 50%\">\\({\\left(6\\right)}^{-2}{\\left({k}^{3}\\right)}^{-2}\\)<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 50%\">Use the Power Property, \\({\\left({a}^{m}\\right)}^{n}={a}^{m\\cdot n}\\).<\/td>\r\n<td style=\"width: 50%\">\\({6}^{-2}{k}^{-6}\\)<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 50%\">Use the Definition of a Negative Exponent, \\({a}^{-n}=\\frac{1}{{a}^{n}}\\).<\/td>\r\n<td style=\"width: 50%\">\\(\\frac{1}{{6}^{2}}\\cdot\\frac{1}{{k}^{6}}\\)<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 50%\">Simplify.<\/td>\r\n<td style=\"width: 50%\">\\(\\frac{1}{36{k}^{6}}\\)<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">TRY IT 11.1<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n<div data-type=\"problem\">\r\n<p id=\"fs-id1169597537101\">Simplify: \\({\\left(-4{x}^{4}\\right)}^{-2}\\).<\/p>\r\n\r\n<\/div>\r\n<div id=\"fs-id1169597537127\" data-type=\"solution\"><details><summary>Show answer<\/summary>\r\n<p id=\"fs-id1169597537129\">\\(\\frac{1}{16{x}^{8}}\\)<\/p>\r\n\r\n<\/details><\/div>\r\n<\/div>\r\n<\/div>\r\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">TRY IT 11.2<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n<div id=\"fs-id1169597478540\" data-type=\"problem\">\r\n<p id=\"fs-id1169597478542\">Simplify: \\({\\left(2{b}^{3}\\right)}^{-4}\\).<\/p>\r\n\r\n<\/div>\r\n<div id=\"fs-id1169597688446\" data-type=\"solution\"><details><summary>Show answer<\/summary>\r\n<p id=\"fs-id1169597688449\">\\(\\frac{1}{16{b}^{12}}\\)<\/p>\r\n\r\n<\/details><\/div>\r\n<\/div>\r\n<\/div>\r\n<div id=\"fs-id1169597537093\" class=\"try\" data-type=\"note\">\r\n<div id=\"fs-id1169597537097\" data-type=\"exercise\">\r\n<div data-type=\"problem\">\r\n<div class=\"textbox textbox--examples\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">EXAMPLE 12<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n<div id=\"fs-id1169597688473\" data-type=\"problem\">\r\n<p id=\"fs-id1169597688475\">Simplify: \\({\\left(5{x}^{-3}\\right)}^{2}\\).<\/p>\r\n\r\n<\/div>\r\n<div data-type=\"solution\">\r\n<div data-type=\"title\"><\/div>\r\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\r\n<div data-type=\"title\">\r\n<table style=\"border-collapse: collapse;width: 100%\" border=\"0\">\r\n<tbody>\r\n<tr>\r\n<td style=\"width: 50%\"><\/td>\r\n<td style=\"width: 50%\">\\({\\left(5{x}^{-3}\\right)}^{2}\\)<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 50%\">Use the Product to a Power Property, \\({\\left(ab\\right)}^{m}={a}^{m}{b}^{m}\\).<\/td>\r\n<td style=\"width: 50%\">\\({5}^{2}{\\left({x}^{-3}\\right)}^{2}\\)<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 50%\">Simplify and multiply the exponents of \\(x\\) using the Power Property, \\({\\left({a}^{m}\\right)}^{n}={a}^{m\\cdot n}\\).<\/td>\r\n<td style=\"width: 50%\">\\(25\\cdot{x}^{-6}\\)<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 50%\">Rewrite by using the Definition of a Negative Exponent, \\({a}^{-n}=\\frac{1}{{a}^{n}}\\).<\/td>\r\n<td style=\"width: 50%\">\\(25\\cdot\\frac{1}{{x}^{6}}\\)<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 50%\">Simplify.<\/td>\r\n<td style=\"width: 50%\">\\(\\frac{25}{{x}^{6}}\\)<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<div id=\"fs-id1169597478534\" class=\"try\" data-type=\"note\">\r\n<div id=\"fs-id1169597478538\" data-type=\"exercise\">\r\n<div id=\"fs-id1169597688446\" data-type=\"solution\">\r\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">TRY IT 12.1<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n<div id=\"fs-id1169597691022\" data-type=\"problem\">\r\n<p id=\"fs-id1169597533022\">Simplify: \\({\\left(8{a}^{-4}\\right)}^{2}\\).<\/p>\r\n\r\n<\/div>\r\n<div data-type=\"solution\"><details><summary>Show answer<\/summary>\r\n<p id=\"fs-id1169597533050\">\\(\\frac{64}{{a}^{8}}\\)<\/p>\r\n\r\n<\/details><\/div>\r\n<\/div>\r\n<\/div>\r\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">TRY IT 12.2<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n<div id=\"fs-id1169597742767\" data-type=\"problem\">\r\n<p id=\"fs-id1169597742769\">Simplify: \\({\\left(2{c}^{-4}\\right)}^{3}\\).<\/p>\r\n\r\n<\/div>\r\n<div id=\"fs-id1169597742794\" data-type=\"solution\"><details><summary>Show answer<\/summary>\r\n<p id=\"fs-id1169597742796\">\\(\\frac{8}{{c}^{12}}\\)<\/p>\r\n\r\n<\/details><\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<div id=\"fs-id1169597533068\" class=\"try\" data-type=\"note\">\r\n<div id=\"fs-id1169597742764\" data-type=\"exercise\">\r\n<div id=\"fs-id1169597742767\" data-type=\"problem\">To simplify a fraction, we use the Quotient Property and subtract the exponents.<\/div>\r\n<\/div>\r\n<\/div>\r\n<div class=\"textbox textbox--examples\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">EXAMPLE 13<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n<div id=\"fs-id1169597537035\" data-type=\"problem\">\r\n<p id=\"fs-id1169597537037\">Simplify: \\(\\frac{{r}^{5}}{{r}^{-4}}\\).<\/p>\r\n\r\n<\/div>\r\n<div data-type=\"solution\">\r\n<div data-type=\"title\"><\/div>\r\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\r\n<div data-type=\"title\">\r\n<table style=\"border-collapse: collapse;width: 100%\" border=\"0\">\r\n<tbody>\r\n<tr>\r\n<td style=\"width: 50%\"><\/td>\r\n<td style=\"width: 50%\">\\(\\frac{{r}^{5}}{{r}^{-4}}\\)<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 50%\">Use the Quotient Property, \\(\\frac{{a}^{m}}{{a}^{n}}={a}^{m-n}\\).<\/td>\r\n<td style=\"width: 50%\">\\({r}^{5-\\left(-4\\right)}\\)<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 50%\">Simplify.<\/td>\r\n<td style=\"width: 50%\">\\({r}^{9}\\)<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">TRY IT 13.1<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n<div id=\"fs-id1169597740300\" data-type=\"problem\">\r\n<p id=\"fs-id1169597740302\">Simplify: \\(\\frac{{x}^{8}}{{x}^{-3}}\\).<\/p>\r\n\r\n<\/div>\r\n<div id=\"fs-id1169597460929\" data-type=\"solution\"><details><summary>Show answer<\/summary>\r\n<p id=\"fs-id1169597460931\">\\({x}^{11}\\)<\/p>\r\n\r\n<\/details><\/div>\r\n<\/div>\r\n<\/div>\r\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">TRY IT 13.2<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n<div data-type=\"problem\">\r\n\r\nSimplify: \\(\\frac{{y}^{8}}{{y}^{-6}}\\).\r\n\r\n<\/div>\r\n<div id=\"fs-id1169597689448\" data-type=\"solution\"><details><summary>Show answer<\/summary>\r\n<p id=\"fs-id1169597689450\">\\({y}^{14}\\)<\/p>\r\n\r\n<\/details><\/div>\r\n<\/div>\r\n<\/div>\r\n<h1>Convert from Decimal Notation to Scientific Notation<\/h1>\r\n<p id=\"fs-id1169597689470\">Remember working with place value for whole numbers and decimals? Our number system is based on powers of 10. We use tens, hundreds, thousands, and so on. Our decimal numbers are also based on powers of tens\u2014tenths, hundredths, thousandths, and so on. Consider the numbers 4,000 and \\(0.004\\). We know that 4,000 means \\(4\\phantom{\\rule{0.2em}{0ex}}\\times\\phantom{\\rule{0.2em}{0ex}}1,000\\) and 0.004 means \\(4\\phantom{\\rule{0.2em}{0ex}}\\times\\phantom{\\rule{0.2em}{0ex}}\\frac{1}{1,000}\\).<\/p>\r\n<p id=\"fs-id1169597740645\">If we write the 1000 as a power of ten in exponential form, we can rewrite these numbers in this way:<\/p>\r\n\r\n<div id=\"fs-id1169597740648\" class=\"unnumbered\" data-type=\"equation\" data-label=\"\">\\(\\begin{array}{cccc}4,000\\hfill &amp; &amp; &amp; \\phantom{\\rule{4em}{0ex}}0.004\\hfill \\\\ 4\\phantom{\\rule{0.2em}{0ex}}\\times\\phantom{\\rule{0.2em}{0ex}}1,000\\hfill &amp; &amp; &amp; \\phantom{\\rule{4em}{0ex}}4\\phantom{\\rule{0.2em}{0ex}}\\times\\phantom{\\rule{0.2em}{0ex}}\\frac{1}{1,000}\\hfill \\\\ 4\\phantom{\\rule{0.2em}{0ex}}\\times\\phantom{\\rule{0.2em}{0ex}}{10}^{3}\\hfill &amp; &amp; &amp; \\phantom{\\rule{4em}{0ex}}4\\phantom{\\rule{0.2em}{0ex}}\\times\\phantom{\\rule{0.2em}{0ex}}\\frac{1}{{10}^{3}}\\hfill \\\\ &amp; &amp; &amp; \\phantom{\\rule{4em}{0ex}}4\\phantom{\\rule{0.2em}{0ex}}\\times\\phantom{\\rule{0.2em}{0ex}}{10}^{-3}\\hfill \\end{array}\\)<\/div>\r\n<p id=\"fs-id1169597742460\">In <em>scientific notation<\/em>, a number is expressed as the product of a coefficient and an exponential expression with a base of 10 and an integer power. The coefficient is a decimal number greater than or equal to 1 but less than 10, and the power of 10 is always an <strong>integer<\/strong>.<\/p>\r\n\r\n<div id=\"fs-id1169597742470\" data-type=\"note\">\r\n<div data-type=\"title\">\r\n<div class=\"textbox textbox--key-takeaways\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">Scientific Notation<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n<p id=\"fs-id1169597742475\">A number is expressed in scientific notation when it is of the form<\/p>\r\n\r\n<div id=\"fs-id1169597742489\" class=\"unnumbered\" data-type=\"equation\" data-label=\"\">\\(\\begin{array}{cccc}&amp; &amp; &amp; a\\phantom{\\rule{0.2em}{0ex}}\\times\\phantom{\\rule{0.2em}{0ex}}{10}^{n}\\phantom{\\rule{0.2em}{0ex}}\\text{where}\\phantom{\\rule{0.2em}{0ex}}1\\le a&lt;10\\phantom{\\rule{0.2em}{0ex}}\\text{and}\\phantom{\\rule{0.2em}{0ex}}n\\phantom{\\rule{0.2em}{0ex}}\\text{is an integer}\\hfill \\end{array}\\)<\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<p id=\"fs-id1169597516025\">It is customary in scientific notation to use as the \\(\\phantom{\\rule{0.2em}{0ex}}\\times\\phantom{\\rule{0.2em}{0ex}}\\) multiplication sign, even though we avoid using this sign elsewhere in algebra.<\/p>\r\n<p id=\"fs-id1169597523393\">If we look at what happened to the decimal point, we can see a method to easily convert from decimal notation to <span class=\"no-emphasis\" data-type=\"term\">scientific notation<\/span>.<\/p>\r\n<span id=\"fs-id1169597523406\" data-type=\"media\" data-alt=\"This figure illustrates how to convert a number to scientific notation. It has two columns. In the first column is 4000 equals 4 times 10 to the third power. Below this, the equation is repeated, with an arrow demonstrating that the decimal point at the end of 4000 has moved three places to the left, so that 4000 becomes 4.000. The second column has 0.004 equals 4 times 10 to the negative third power. Below this, the equation is repeated, with an arrow demonstrating how the decimal point in 0.004 is moved three places to the right to produce 4.\"><img class=\"aligncenter\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/uploads\/sites\/1441\/2021\/06\/CNX_ElemAlg_Figure_06_07_002_img_new.jpg\" alt=\"This figure illustrates how to convert a number to scientific notation. It has two columns. In the first column is 4000 equals 4 times 10 to the third power. Below this, the equation is repeated, with an arrow demonstrating that the decimal point at the end of 4000 has moved three places to the left, so that 4000 becomes 4.000. The second column has 0.004 equals 4 times 10 to the negative third power. Below this, the equation is repeated, with an arrow demonstrating how the decimal point in 0.004 is moved three places to the right to produce 4.\" data-media-type=\"image\/jpeg\" \/><\/span>\r\n<p id=\"fs-id1169597523423\">In both cases, the decimal was moved 3 places to get the coefficient between 1 and 10<\/p>\r\n<p id=\"fs-id1169594046599\">\\(\\begin{array}{cccc}\\text{The power of 10 is positive when the number is larger than 1:}\\hfill &amp; &amp; &amp; 4,000=4\\phantom{\\rule{0.2em}{0ex}}\\times\\phantom{\\rule{0.2em}{0ex}}{10}^{3}\\hfill \\\\ \\text{The power of 10 is negative when the number is between 0 and 1:}\\hfill &amp; &amp; &amp; 0.004=4\\phantom{\\rule{0.2em}{0ex}}\\times\\phantom{\\rule{0.2em}{0ex}}{10}^{-3}\\hfill \\end{array}\\)<\/p>\r\n\r\n<div class=\"textbox textbox--examples\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">EXAMPLE 14<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n<div data-type=\"title\">How to Convert from Decimal Notation to Scientific Notation<\/div>\r\n<div id=\"fs-id1169597691148\" data-type=\"exercise\">\r\n<div id=\"fs-id1169597691150\" data-type=\"problem\">\r\n<p id=\"fs-id1169597691152\">Write in scientific notation: 37,000.<\/p>\r\n\r\n<\/div>\r\n<div id=\"fs-id1169597691157\" data-type=\"solution\">\r\n<div data-type=\"title\"><\/div>\r\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\r\n<div data-type=\"title\">\r\n<table style=\"border-collapse: collapse;width: 100%\" border=\"0\">\r\n<tbody>\r\n<tr>\r\n<td style=\"width: 59.4523%\">Step 1. Identify the decimal point's current position in the number: In this case, the decimal point is after the last digit, so it's located at the end of the number.<\/td>\r\n<td style=\"width: 40.5477%\">[latex]37,000 \\color{red}{\\scalebox{2}{.}}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 59.4523%\">Step2. Count the number of places you need to move the decimal point to make the number between 1 and 10: In this case, you need to move the decimal point 4 places to the left.<\/td>\r\n<td style=\"width: 40.5477%\"><a href=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/uploads\/sites\/1441\/2021\/05\/Screenshot-2023-06-22-112012.jpg\"><img class=\"alignnone size-full wp-image-2628\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/uploads\/sites\/1441\/2021\/05\/Screenshot-2023-06-22-112012.jpg\" alt=\"\" width=\"72\" height=\"64\" \/><\/a><\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 59.4523%\">Step 3. Write the number as a decimal between 1 and 10, followed by the multiplication symbol[latex] (\\times)[\/latex] and 10 raised to the power of the number of places the decimal point moved:\r\n<ul>\r\n \t<li style=\"list-style-type: none\">\r\n<ul>\r\n \t<li>Decimal between 1 and 10: <strong>3.7<\/strong> (move the decimal point from 37000 four places to the left)<\/li>\r\n \t<li>Power of 10: [latex]10^4[\/latex]<\/li>\r\n<\/ul>\r\n<\/li>\r\n<\/ul>\r\n<\/td>\r\n<td style=\"width: 40.5477%\">[latex]3.7 \\times 10^{4}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 59.4523%\">Step 4. Check: Check to see if your answer makes sense.<\/td>\r\n<td style=\"width: 40.5477%\">[latex]10^4[\/latex] is 10,000\r\nand\r\n[latex]10,000 \\times 3.7[\/latex] will be [latex]37,000[\/latex] .<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">TRY IT 14.1<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n<div id=\"fs-id1169597536011\" data-type=\"problem\">\r\n<p id=\"fs-id1169597536013\">Write in scientific notation: \\(96,000\\).<\/p>\r\n\r\n<\/div>\r\n<div id=\"fs-id1169597536022\" data-type=\"solution\"><details open=\"open\"><summary>Show answer<\/summary>\r\n<p id=\"fs-id1169597536024\">\\(9.6\\phantom{\\rule{0.2em}{0ex}}\\times\\phantom{\\rule{0.2em}{0ex}}{10}^{4}\\)<\/p>\r\n\r\n<\/details><\/div>\r\n<\/div>\r\n<\/div>\r\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">TRY IT 14.2<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n<div id=\"fs-id1169597536048\" data-type=\"problem\">\r\n<p id=\"fs-id1169597536050\">Write in scientific notation: \\(48,300\\).<\/p>\r\n\r\n<\/div>\r\n<div id=\"fs-id1169597536063\" data-type=\"solution\"><details open=\"open\"><summary>Show answer<\/summary>\r\n<p id=\"fs-id1169597701072\">\\(4.83\\phantom{\\rule{0.2em}{0ex}}\\times\\phantom{\\rule{0.2em}{0ex}}{10}^{4}\\)<\/p>\r\n\r\n<\/details><\/div>\r\n<\/div>\r\n<\/div>\r\n<div class=\"textbox textbox--key-takeaways\"><header class=\"textbox__header\">HOW TO: Convert from decimal notation to scientific notation<\/header>\r\n<div class=\"textbox__content\">\r\n<ol id=\"fs-id1168743403951\" class=\"stepwise\" type=\"1\">\r\n \t<li>Move the decimal point so that the first number is greater than or equal to 1 but less than 10.<\/li>\r\n \t<li>Count the number of decimal places, <em data-effect=\"italics\">n<\/em>, that the decimal point was moved.<\/li>\r\n \t<li>Write the number as a product with a power of 10.\r\nIf the original number is:\r\n<ul id=\"fs-id1168744092452\" data-bullet-style=\"bullet\">\r\n \t<li>greater than 1, the power of 10 will be 10<sup><em data-effect=\"italics\">n<\/em><\/sup>.<\/li>\r\n \t<li>between 0 and 1, the power of 10 will be 10<sup><em data-effect=\"italics\">\u2212n<\/em><\/sup>.<\/li>\r\n<\/ul>\r\n<\/li>\r\n \t<li>Check.<\/li>\r\n<\/ol>\r\n<\/div>\r\n<\/div>\r\n<div id=\"fs-id1168743403943\" class=\"howto\" data-type=\"note\">\r\n<div class=\"textbox textbox--examples\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">EXAMPLE 15<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n<div id=\"fs-id1169597701094\" data-type=\"problem\">\r\n<p id=\"fs-id1169597701096\">Write in scientific notation: \\(0.0052\\).<\/p>\r\n\r\n<\/div>\r\n<div id=\"fs-id1169597701105\" data-type=\"solution\">\r\n<div data-type=\"title\"><\/div>\r\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\r\n<div data-type=\"title\"><\/div>\r\n<p id=\"fs-id1169597701107\">The original number, \\(0.0052\\), is between 0 and 1 so we will have a negative power of 10<\/p>\r\n\r\n<table style=\"border-collapse: collapse;width: 100%;height: 115px\" border=\"0\">\r\n<tbody>\r\n<tr style=\"height: 25px\">\r\n<td style=\"width: 50%;height: 25px\"><\/td>\r\n<td style=\"width: 50%;height: 25px\"><span id=\"eip-id1172181050459\" data-type=\"media\" data-alt=\"0.0052.\">[latex]0{\\color{red}{\\scalebox{2}{.}}}0052[\/latex]<\/span><\/td>\r\n<\/tr>\r\n<tr style=\"height: 15px\">\r\n<td style=\"width: 50%;height: 15px\">Move the decimal point to get 5.2, a number between 1 and 10.<\/td>\r\n<td style=\"width: 50%;height: 15px\"><span id=\"eip-id1172181050475\" data-type=\"media\" data-alt=\"0.0052, with an arrow showing the decimal point jumping three places to the right until it ends up between the 5 and 2.\"><img class=\"aligncenter\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/uploads\/sites\/1441\/2021\/06\/CNX_ElemAlg_Figure_06_07_004b_img_new.jpg\" alt=\"0.0052, with an arrow showing the decimal point jumping three places to the right until it ends up between the 5 and 2.\" width=\"119\" height=\"17\" data-media-type=\"image\/png\" \/><\/span><\/td>\r\n<\/tr>\r\n<tr style=\"height: 15px\">\r\n<td style=\"width: 50%;height: 15px\">Count the number of decimal places the point was moved.<\/td>\r\n<td style=\"width: 50%;height: 15px\"><span id=\"eip-id1172181050492\" data-type=\"media\" data-alt=\"3 places.\">3 places<\/span><\/td>\r\n<\/tr>\r\n<tr style=\"height: 15px\">\r\n<td style=\"width: 50%;height: 15px\">Write as a product with a power of 10.<\/td>\r\n<td style=\"width: 50%;height: 15px\"><span id=\"eip-id1172181050509\" data-type=\"media\" data-alt=\"5.2 times 10 to the power of negative 3.\">[latex]5.2 \\times 10^{-3}[\/latex]<\/span><\/td>\r\n<\/tr>\r\n<tr style=\"height: 15px\">\r\n<td style=\"width: 50%;height: 15px\">Check.<\/td>\r\n<td style=\"width: 50%;height: 15px\">\\(\\begin{array}{ccccc}\\\\ \\\\ \\phantom{\\rule{3em}{0ex}}5.2\\phantom{\\rule{0.2em}{0ex}}\\times\\phantom{\\rule{0.2em}{0ex}}{10}^{-3}\\hfill \\\\ \\phantom{\\rule{3em}{0ex}}=5.2\\phantom{\\rule{0.2em}{0ex}}\\times\\phantom{\\rule{0.2em}{0ex}}\\frac{1}{{10}^{3}}\\hfill \\\\ \\phantom{\\rule{3em}{0ex}}=5.2\\phantom{\\rule{0.2em}{0ex}}\\times\\phantom{\\rule{0.2em}{0ex}}\\frac{1}{1000} \\\\ \\phantom{\\rule{3em}{0ex}}=5.2\\phantom{\\rule{0.2em}{0ex}}\\times\\phantom{\\rule{0.2em}{0ex}}0.001\\hfill \\\\ \\(\\phantom{\\rule{2 em}{0 ex}}=0.0052 \\checkmark \\end{array}\\)<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">TRY IT 15.1<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n<div id=\"fs-id1169597577078\" data-type=\"problem\">\r\n<p id=\"fs-id1169597577080\">Write in scientific notation: \\(0.0078\\).<\/p>\r\n\r\n<\/div>\r\n<div id=\"fs-id1169597577089\" data-type=\"solution\"><details open=\"open\"><summary>Show answer<\/summary>\r\n<p id=\"fs-id1169597577091\">\\(7.8\\phantom{\\rule{0.2em}{0ex}}\\times\\phantom{\\rule{0.2em}{0ex}}{10}^{-3}\\)<\/p>\r\n\r\n<\/details><\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<div id=\"fs-id1169597701126\" class=\"try\" data-type=\"note\">\r\n<div id=\"fs-id1169597577076\" data-type=\"exercise\">\r\n<div id=\"fs-id1169597577089\" data-type=\"solution\">\r\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">TRY IT 15.2<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n<div id=\"fs-id1169597577116\" data-type=\"problem\">\r\n<p id=\"fs-id1169597577118\">Write in scientific notation: \\(0.0129\\).<\/p>\r\n\r\n<\/div>\r\n<div id=\"fs-id1169597577127\" data-type=\"solution\"><details open=\"open\"><summary>Show answer<\/summary>\r\n<p id=\"fs-id1169597555672\">\\(1.29\\phantom{\\rule{0.2em}{0ex}}\\times\\phantom{\\rule{0.2em}{0ex}}{10}^{-2}\\)<\/p>\r\n\r\n<\/details><\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<h1>Convert Scientific Notation to Decimal Form<\/h1>\r\n<p id=\"fs-id1169597555698\">How can we convert from scientific notation to decimal form? Let\u2019s look at two numbers written in scientific notation and see.<\/p>\r\n\r\n<div id=\"fs-id1169597555702\" class=\"unnumbered\" data-type=\"equation\" data-label=\"\">\\(\\begin{array}{cccc}\\hfill 9.12\\phantom{\\rule{0.2em}{0ex}}\\times\\phantom{\\rule{0.2em}{0ex}}{10}^{4}\\hfill &amp; &amp; &amp; \\hfill \\phantom{\\rule{4em}{0ex}}9.12\\phantom{\\rule{0.2em}{0ex}}\\times\\phantom{\\rule{0.2em}{0ex}}{10}^{-4}\\hfill \\\\ \\hfill 9.12\\phantom{\\rule{0.2em}{0ex}}\\times\\phantom{\\rule{0.2em}{0ex}}10,000\\hfill &amp; &amp; &amp; \\hfill \\phantom{\\rule{4em}{0ex}}9.12\\phantom{\\rule{0.2em}{0ex}}\\times\\phantom{\\rule{0.2em}{0ex}}0.0001\\hfill \\\\ \\hfill 91,200\\hfill &amp; &amp; &amp; \\hfill \\phantom{\\rule{4em}{0ex}}0.000912\\hfill \\end{array}\\)<\/div>\r\n<p id=\"fs-id1169597688301\">If we look at the location of the decimal point, we can see an easy method to convert a number from scientific notation to decimal form.<\/p>\r\n\r\n<div class=\"unnumbered\" data-type=\"equation\" data-label=\"\">\\(\\begin{array}{cccc}\\hfill 9.12\\phantom{\\rule{0.2em}{0ex}}\\times\\phantom{\\rule{0.2em}{0ex}}{10}^{4}=91,200\\hfill &amp; &amp; &amp; \\hfill \\phantom{\\rule{4em}{0ex}}9.12\\phantom{\\rule{0.2em}{0ex}}\\times\\phantom{\\rule{0.2em}{0ex}}{10}^{-4}=0.000912\\hfill \\end{array}\\)<\/div>\r\n<span id=\"fs-id1169597742376\" data-type=\"media\" data-alt=\"This figure has two columns. In the left column is 9.12 times 10 to the fourth power equals 91,200. Below this, the same scientific notation is repeated, with an arrow showing the decimal point in 9.12 being moved four places to the right. Because there are no digits after 2, the final two places are represented by blank spaces. Below this is the text \u201cMove the decimal point four places to the right.\u201d In the right column is 9.12 times 10 to the negative fourth power equals 0.000912. Below this, the same scientific notation is repeated, with an arrow showing the decimal point in 9.12 being moved four places to the left. Because there are no digits before 9, the remaining three places are represented by spaces. Below this is the text \u201cMove the decimal point 4 places to the left.\u201d\"><img class=\"aligncenter\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/uploads\/sites\/1441\/2021\/06\/CNX_ElemAlg_Figure_06_02_015_img.jpg\" alt=\"This figure has two columns. In the left column is 9.12 times 10 to the fourth power equals 91,200. Below this, the same scientific notation is repeated, with an arrow showing the decimal point in 9.12 being moved four places to the right. Because there are no digits after 2, the final two places are represented by blank spaces. Below this is the text \u201cMove the decimal point four places to the right.\u201d In the right column is 9.12 times 10 to the negative fourth power equals 0.000912. Below this, the same scientific notation is repeated, with an arrow showing the decimal point in 9.12 being moved four places to the left. Because there are no digits before 9, the remaining three places are represented by spaces. Below this is the text \u201cMove the decimal point 4 places to the left.\u201d\" data-media-type=\"image\/jpeg\" \/><\/span>\r\n<p id=\"fs-id1169597742371\">In both cases the decimal point moved 4 places. When the exponent was positive, the decimal moved to the right. When the exponent was negative, the decimal point moved to the left.<\/p>\r\n\r\n<div class=\"textbox textbox--examples\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">EXAMPLE 16<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n<div data-type=\"title\">How to Convert Scientific Notation to Decimal Form<\/div>\r\n<div id=\"fs-id1169597741743\" data-type=\"exercise\">\r\n<div id=\"fs-id1169597741745\" data-type=\"problem\">\r\n<p id=\"fs-id1169597741747\">Convert to decimal form: \\(6.2\\phantom{\\rule{0.2em}{0ex}}\\times\\phantom{\\rule{0.2em}{0ex}}{10}^{3}\\).<\/p>\r\n\r\n<\/div>\r\n<div id=\"fs-id1169597741764\" data-type=\"solution\">\r\n<div data-type=\"title\"><\/div>\r\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\r\n<div data-type=\"title\">\r\n<table style=\"border-collapse: collapse;width: 100%;height: 149px\" border=\"0\" data-alt=\"This figure is a table that has three columns and three rows. The first column is a header column, and it contains the names and numbers of each step. The second column contains further written instructions. The third column contains math. On the top row of the table, the first cell on the left reads \u201cStep 1. Determine the exponent, n, on the factor 10.\u201d The second cell reads \u201cThe exponent is 3.\u201d The third cell contains 6.2 times 10 cubed. In the second row, the first cell reads \u201cStep 2. Move the decimal n places, adding zeros if needed. If the exponent is positive, move the decimal point n places to the right. If the exponent is negative, move the decimal point absolute value of n places to the left.\u201d The second cell reads \u201cThe exponent is positive so move the decimal point 3 places to the right. We need to add two zeros as placeholders.\u201d The third cell contains 6.200, with an arrow showing the decimal point jumping places to the right, from between the 6 and 2 to after the second 00 in 6.200. Below this is the number 6,200. In the third row, the first cell reads \u201cStep 3. Check to see if your answer makes sense.\u201d The second cell is blank. The third reads \u201c10 cubed is 1000 and 1000 times 6.2 will be 6,200.\u201d Beneath this is 6.2 times 10 cubed equals 6,200.\">\r\n<tbody>\r\n<tr style=\"height: 33px\">\r\n<td style=\"width: 33.3333%;height: 33px\">Step 1. Determine the exponent, [latex]n[\/latex] on the factor [latex]10[\/latex].<\/td>\r\n<td style=\"width: 33.3333%;height: 33px\">The exponent is [latex]3[\/latex].<\/td>\r\n<td style=\"width: 33.3333%;height: 33px\">[latex]6.2 \\times 10^3[\/latex]<\/td>\r\n<\/tr>\r\n<tr style=\"height: 116px\">\r\n<td style=\"width: 33.3333%;height: 116px\">\r\n<div>Step 2. Move the decimal [latex]n[\/latex] places, adding zeros if needed.<\/div>\r\n<div><\/div>\r\n<div>If the exponent is positive, move the decimal point [latex]n[\/latex] places to the right.<\/div>\r\n<div><\/div>\r\n<div>If the exponent is negative, move the decimal point [latex] |n|[\/latex] places to the left.<\/div><\/td>\r\n<td style=\"width: 33.3333%;height: 116px\">The exponent is positive, so move the decimal point 3 places to the right. We need to add 2 zeros as placeholders.<\/td>\r\n<td style=\"width: 33.3333%;height: 116px\"><a href=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/uploads\/sites\/1441\/2021\/05\/EX16_img1.jpg\"><img class=\"alignnone size-full wp-image-2792\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/uploads\/sites\/1441\/2021\/05\/EX16_img1.jpg\" alt=\"\" width=\"56\" height=\"51\" \/><\/a> [latex]=6,200[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 33.3333%\">\r\n<div>Step 3. Check to see if your answer makes sense.<\/div><\/td>\r\n<td style=\"width: 33.3333%\">[latex]10^3[\/latex] is [latex]1000[\/latex] and [latex]1000[\/latex] times [latex]6.2 [\/latex] will be [latex]6,200[\/latex].<\/td>\r\n<td style=\"width: 33.3333%\">[latex]6.2 \\times 10^3=6,200 \\checkmark [\/latex]<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">TRY IT 16.1<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n<div id=\"fs-id1169597741410\" data-type=\"problem\">\r\n<p id=\"fs-id1169597741412\">Convert to decimal form: \\(1.3\\phantom{\\rule{0.2em}{0ex}}\\times\\phantom{\\rule{0.2em}{0ex}}{10}^{3}\\).<\/p>\r\n\r\n<\/div>\r\n<div id=\"fs-id1169597741429\" data-type=\"solution\"><details open=\"open\"><summary>Show answer<\/summary>\r\n<p id=\"fs-id1169597741431\">1,300<\/p>\r\n\r\n<\/details><\/div>\r\n<\/div>\r\n<\/div>\r\n<div id=\"fs-id1169597741404\" class=\"try\" data-type=\"note\">\r\n<div id=\"fs-id1169597741408\" data-type=\"exercise\">\r\n<div id=\"fs-id1169597741429\" data-type=\"solution\">\r\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">TRY IT 16.2<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n<div id=\"fs-id1169597741444\" data-type=\"problem\">\r\n<p id=\"fs-id1169597741446\">Convert to decimal form: \\(9.25\\phantom{\\rule{0.2em}{0ex}}\\times\\phantom{\\rule{0.2em}{0ex}}{10}^{4}\\).<\/p>\r\n\r\n<\/div>\r\n<div id=\"fs-id1169597505400\" data-type=\"solution\"><details open=\"open\"><summary>Show answer<\/summary>\r\n<p id=\"fs-id1169597505402\">92,500<\/p>\r\n\r\n<\/details><\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<p id=\"fs-id1169597505408\">The steps are summarized below.<\/p>\r\n\r\n<div class=\"textbox textbox--key-takeaways\"><header class=\"textbox__header\">HOW TO: Convert scientific notation to decimal form.<\/header>\r\n<div class=\"textbox__content\">\r\n<p id=\"fs-id1169597505421\">To convert scientific notation to decimal form:<\/p>\r\n\r\n<ol id=\"fs-id1168746296183\" class=\"stepwise\" type=\"1\">\r\n \t<li>Identify the exponent, \\(n\\), that represents the power of 10 in the scientific notation.<\/li>\r\n \t<li>Move the decimal \\(n\\) places, adding zeros if needed.\r\n<ul id=\"fs-id1169597505448\" data-bullet-style=\"bullet\">\r\n \t<li>If the exponent is positive, move the decimal point \\(n\\) places to the right.<\/li>\r\n \t<li>If the exponent is negative, move the decimal point \\(|n|\\) places to the left.<\/li>\r\n<\/ul>\r\n<\/li>\r\n \t<li>Check.<\/li>\r\n<\/ol>\r\n<\/div>\r\n<\/div>\r\n<div id=\"fs-id1169597505412\" class=\"howto\" data-type=\"note\">\r\n<div class=\"textbox textbox--examples\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">EXAMPLE 17<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n<div id=\"fs-id1169597744324\" data-type=\"problem\">\r\n<p id=\"fs-id1169597744326\">Convert to decimal form: \\(8.9\\phantom{\\rule{0.2em}{0ex}}\\times\\phantom{\\rule{0.2em}{0ex}}{10}^{-2}\\).<\/p>\r\n\r\n<\/div>\r\n<div id=\"fs-id1169597744344\" data-type=\"solution\">\r\n<div data-type=\"title\"><\/div>\r\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\r\n<table id=\"eip-id1172187383117\" class=\"unnumbered unstyled\" style=\"width: 100%\" summary=\"This figure has two columns. At the top of the figure, in the right column is 8.9 times 10 to the negative second power. One row down, the text in the left column says \u201cDetermine the exponent, n, on the factor 10.\u201d The right column says \u201cThe exponent is negative 2.\u201d One row down, the text in the left column says \u201cSince the exponent is negative, move the decimal point 2 places to the left.\u201d The right column contains 8.9, with an arrow showing the decimal point in 9.12 being moved two places to the left. Because there are no digits before 8, the remaining places are represented by spaces. One row down, the text in the left says \u201cAdd zeros as needed for placeholders.\u201d The right column contains 8.9 times 10 to the negative second power equals 0.089.\" data-label=\"\">\r\n<tbody>\r\n<tr>\r\n<td style=\"width: 60%\"><\/td>\r\n<td style=\"width: 40%\">[latex]8.9 \\times 10^{-2}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 60%\">Identify the exponent, \\(n\\), that represents the power of 10 in the scientific notation.<\/td>\r\n<td style=\"width: 40\">The exponent is [latex]-2[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 60%\">Since the exponent is negative, move the decimal point 2 places to the left.<\/td>\r\n<td style=\"width: 40%\"><span id=\"eip-id1172187383169\" data-type=\"media\" data-alt=\"8.9, with an arrow the decimal place showing the decimal point being moved two places to the left.\"><img src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/uploads\/sites\/1441\/2021\/06\/CNX_ElemAlg_Figure_06_07_007c_img_new.jpg\" alt=\"8.9, with an arrow the decimal place showing the decimal point being moved two places to the left.\" data-media-type=\"image\/png\" \/><\/span><\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 60%\">Add zeros as needed for placeholders.<\/td>\r\n<td style=\"width: 40%\">[latex]8.9 \\times 10^{-2} = 0.089[\/latex]<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">TRY IT 17.1<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n<div id=\"fs-id1169597739737\" data-type=\"problem\">\r\n<p id=\"fs-id1169597739739\">Convert to decimal form: \\(1.2\\phantom{\\rule{0.2em}{0ex}}\\times\\phantom{\\rule{0.2em}{0ex}}{10}^{-4}\\).<\/p>\r\n\r\n<\/div>\r\n<div id=\"fs-id1169597739758\" data-type=\"solution\"><details open=\"open\"><summary>Show answer<\/summary>\r\n<p id=\"fs-id1169597739760\">0.00012<\/p>\r\n\r\n<\/details><\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<div id=\"fs-id1169597744367\" class=\"try\" data-type=\"note\">\r\n<div id=\"fs-id1169597744371\" data-type=\"exercise\">\r\n<div id=\"fs-id1169597739758\" data-type=\"solution\">\r\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">TRY IT 17.2<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n<div id=\"fs-id1169597739772\" data-type=\"problem\">\r\n<p id=\"fs-id1169597739774\">Convert to decimal form: \\(7.5\\phantom{\\rule{0.2em}{0ex}}\\times\\phantom{\\rule{0.2em}{0ex}}{10}^{-2}\\).<\/p>\r\n\r\n<\/div>\r\n<div id=\"fs-id1169597739793\" data-type=\"solution\"><details open=\"open\"><summary>Show answer<\/summary>\r\n<p id=\"fs-id1169597739795\">0.075<\/p>\r\n\r\n<\/details><\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<h1>Multiply and Divide Using Scientific Notation<\/h1>\r\n<p id=\"fs-id1169597704318\">Astronomers use very large numbers to describe distances in the universe and ages of stars and planets. Chemists use very small numbers to describe the size of an atom or the charge on an electron. When scientists perform calculations with very large or very small numbers, they use scientific notation. Scientific notation provides a way for the calculations to be done without writing a lot of zeros. We will see how the Properties of Exponents are used to multiply and divide numbers in scientific notation.<\/p>\r\n\r\n<div class=\"textbox textbox--examples\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">EXAMPLE 18<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n<div id=\"fs-id1169597704330\" data-type=\"problem\">\r\n<p id=\"fs-id1169597704332\">Multiply. Write answers in decimal form: \\(\\left(4\\phantom{\\rule{0.2em}{0ex}}\\times\\phantom{\\rule{0.2em}{0ex}}{10}^{5}\\right)\\left(2\\phantom{\\rule{0.2em}{0ex}}\\times\\phantom{\\rule{0.2em}{0ex}}{10}^{-7}\\right)\\).<\/p>\r\n\r\n<\/div>\r\n<div id=\"fs-id1169597704374\" data-type=\"solution\">\r\n<div data-type=\"title\"><\/div>\r\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\r\n<div data-type=\"title\">\r\n<table style=\"border-collapse: collapse;width: 100%;height: 56px\" border=\"0\">\r\n<tbody>\r\n<tr style=\"height: 14px\">\r\n<td style=\"width: 50%;height: 14px\"><\/td>\r\n<td style=\"width: 50%;height: 14px\">\\(\\left(4\\times{10}^{5}\\right)\\left(2\\times{10}^{-7}\\right)\\)<\/td>\r\n<\/tr>\r\n<tr style=\"height: 14px\">\r\n<td style=\"width: 50%;height: 14px\">Use the Commutative Property to rearrange the factors.<\/td>\r\n<td style=\"width: 50%;height: 14px\">\\(4\\cdot 2\\cdot{10}^{5}\\cdot{10}^{-7}\\)<\/td>\r\n<\/tr>\r\n<tr style=\"height: 14px\">\r\n<td style=\"width: 50%;height: 14px\">Multiply.<\/td>\r\n<td style=\"width: 50%;height: 14px\">\\(8\\times{10}^{-2}\\)<\/td>\r\n<\/tr>\r\n<tr style=\"height: 14px\">\r\n<td style=\"width: 50%;height: 14px\">Change to decimal form by moving the decimal two places left.<\/td>\r\n<td style=\"width: 50%;height: 14px\">\\(0.08\\)<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">TRY IT 18.1<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n<div id=\"fs-id1169597576869\" data-type=\"problem\">\r\n<p id=\"fs-id1169597576871\">Multiply \\(\\left(3\\phantom{\\rule{0.2em}{0ex}}\\times\\phantom{\\rule{0.2em}{0ex}}{10}^{6}\\right)\\left(2\\phantom{\\rule{0.2em}{0ex}}\\times\\phantom{\\rule{0.2em}{0ex}}{10}^{-8}\\right)\\). Write answers in decimal form.<\/p>\r\n\r\n<\/div>\r\n<div id=\"fs-id1169597533136\" data-type=\"solution\"><details open=\"open\"><summary>Show answer<\/summary>\r\n<p id=\"fs-id1169597533139\">0.06<\/p>\r\n\r\n<\/details><\/div>\r\n<\/div>\r\n<\/div>\r\n<div id=\"fs-id1169597576863\" class=\"try\" data-type=\"note\">\r\n<div id=\"fs-id1169597576867\" data-type=\"exercise\">\r\n<div id=\"fs-id1169597533136\" data-type=\"solution\">\r\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">TRY IT 18.2<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n<div id=\"fs-id1169597533151\" data-type=\"problem\">\r\n<p id=\"fs-id1169597533153\">Multiply \\(\\left(3\\phantom{\\rule{0.2em}{0ex}}\\times\\phantom{\\rule{0.2em}{0ex}}{10}^{-2}\\right)\\left(3\\phantom{\\rule{0.2em}{0ex}}\\times\\phantom{\\rule{0.2em}{0ex}}{10}^{-1}\\right)\\). Write answers in decimal form.<\/p>\r\n\r\n<\/div>\r\n<div id=\"fs-id1169597705332\" data-type=\"solution\"><details open=\"open\"><summary>Show answer<\/summary>\r\n<p id=\"fs-id1169597705334\">0.009<\/p>\r\n\r\n<\/details><\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<div id=\"fs-id1169597533145\" class=\"try\" data-type=\"note\">\r\n<div id=\"fs-id1169597533149\" data-type=\"exercise\">\r\n<div id=\"fs-id1169597705332\" data-type=\"solution\">\r\n<div class=\"textbox textbox--examples\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">EXAMPLE 19<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n<div id=\"fs-id1169597705345\" data-type=\"problem\">\r\n<p id=\"fs-id1169597705347\">Divide. Write answers in decimal form: \\(\\frac{9\\phantom{\\rule{0.2em}{0ex}}\\times\\phantom{\\rule{0.2em}{0ex}}{10}^{3}}{3\\phantom{\\rule{0.2em}{0ex}}\\times\\phantom{\\rule{0.2em}{0ex}}{10}^{-2}}\\).<\/p>\r\n\r\n<\/div>\r\n<div id=\"fs-id1169597705379\" data-type=\"solution\">\r\n<div data-type=\"title\"><\/div>\r\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\r\n<div data-type=\"title\">\r\n<table style=\"border-collapse: collapse;width: 100%\" border=\"0\">\r\n<tbody>\r\n<tr>\r\n<td style=\"width: 50%\"><\/td>\r\n<td style=\"width: 50%\">\\(\\frac{9\\times{10}^{3}}{3\\times{10}^{-2}}\\)<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 50%\">Rewrite as the product of two fractions.<\/td>\r\n<td style=\"width: 50%\">\\(\\frac{9}{3}\\times\\frac{{10}^{3}}{{10}^{-2}}\\)<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 50%\">Divide.<\/td>\r\n<td style=\"width: 50%\">\\(3\\times{10}^{5}\\)<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 50%\">Change to decimal form by moving the decimal five places right.<\/td>\r\n<td style=\"width: 50%\">\\(300,000\\)<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">TRY IT 19.1<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n<div id=\"fs-id1169597539393\" data-type=\"problem\">\r\n<p id=\"fs-id1169597539395\">Divide \\(\\frac{8\\phantom{\\rule{0.2em}{0ex}}\\times\\phantom{\\rule{0.2em}{0ex}}{10}^{4}}{2\\phantom{\\rule{0.2em}{0ex}}\\times\\phantom{\\rule{0.2em}{0ex}}{10}^{-1}}\\). Write answers in decimal form.<\/p>\r\n\r\n<\/div>\r\n<div id=\"fs-id1169597539428\" data-type=\"solution\"><details open=\"open\"><summary>Show answer<\/summary>\r\n<p id=\"fs-id1169597539431\">400,000<\/p>\r\n\r\n<\/details><\/div>\r\n<\/div>\r\n<\/div>\r\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">TRY IT 19.2<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n<div id=\"fs-id1169597539443\" data-type=\"problem\">\r\n<p id=\"fs-id1169597539445\">Divide \\(\\frac{8\\phantom{\\rule{0.2em}{0ex}}\\times\\phantom{\\rule{0.2em}{0ex}}{10}^{2}}{4\\phantom{\\rule{0.2em}{0ex}}\\times\\phantom{\\rule{0.2em}{0ex}}{10}^{-2}}\\). Write answers in decimal form.<\/p>\r\n\r\n<\/div>\r\n<div id=\"fs-id1169597739980\" data-type=\"solution\"><details open=\"open\"><summary>Show answer<\/summary>\r\n<p id=\"fs-id1169597739982\">20,000<\/p>\r\n\r\n<\/details><\/div>\r\n<\/div>\r\n<\/div>\r\nAccess these online resources for additional instruction and practice with integer exponents and scientific notation:\r\n\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<div id=\"fs-id1169597739988\" class=\"media-2\" data-type=\"note\">\r\n<ul id=\"fs-id1169597739997\" data-display=\"block\">\r\n \t<li><a href=\"https:\/\/openstax.org\/l\/25Negexponents\">Negative Exponents<\/a><\/li>\r\n \t<li><a href=\"https:\/\/openstax.org\/l\/25Scientnot1\">Scientific Notation<\/a><\/li>\r\n \t<li><a href=\"https:\/\/openstax.org\/l\/25Scientnot2\">Scientific Notation 2<\/a><\/li>\r\n<\/ul>\r\n<\/div>\r\n<h1>Key Concepts<\/h1>\r\n<ul id=\"fs-id1169597689120\" data-bullet-style=\"bullet\">\r\n \t<li><strong data-effect=\"bold\">Property of Negative Exponents<\/strong>\r\n<ul id=\"fs-id1169597689133\" data-bullet-style=\"open-circle\">\r\n \t<li>If \\(n\\) is a positive integer and \\(a\\ne 0\\), then \\(\\frac{1}{{a}^{-n}}={a}^{n}\\)<\/li>\r\n<\/ul>\r\n<\/li>\r\n \t<li><strong data-effect=\"bold\">Quotient to a Negative Exponent<\/strong>\r\n<ul id=\"fs-id1169597689185\" data-bullet-style=\"open-circle\">\r\n \t<li>If \\(a,b\\) are real numbers, \\(b\\ne 0\\) and \\(n\\) is an integer , then \\({\\left(\\frac{a}{b}\\right)}^{-n}={\\left(\\frac{b}{a}\\right)}^{n}\\)<\/li>\r\n<\/ul>\r\n<\/li>\r\n \t<li><strong data-effect=\"bold\">To convert a decimal to scientific notation:<\/strong>\r\n<ol id=\"fs-id1168746309069\" class=\"stepwise\" type=\"1\">\r\n \t<li>Move the decimal point so that the coefficient is greater than or equal to 1 but less than 10.<\/li>\r\n \t<li>Count the number of decimal places, \\(n\\), that the decimal point was moved.<\/li>\r\n \t<li>Write the number as a product with a power of 10. If the original number is:\r\n<ul id=\"fs-id1169596704515\" data-bullet-style=\"open-circle\">\r\n \t<li>greater than 1, the power of 10 will be \\({10}^{n}\\)<\/li>\r\n \t<li>between 0 and 1, the power of 10 will be \\({10}^{-n}\\)<\/li>\r\n<\/ul>\r\n<\/li>\r\n \t<li>Check.<\/li>\r\n<\/ol>\r\n<\/li>\r\n \t<li><strong data-effect=\"bold\">To convert scientific notation to decimal form:<\/strong>\r\n<ol id=\"fs-id1168744116887\" class=\"stepwise\" type=\"1\">\r\n \t<li>Identify the exponent, denoted as \\(n\\), that represents the power of 10 in the scientific notation.<\/li>\r\n \t<li>Move the decimal \\(n\\) places, adding zeros if needed.\r\n<ul id=\"fs-id1169597742509\" data-bullet-style=\"open-circle\">\r\n \t<li>If the exponent is positive, move the decimal point \\(n\\) places to the right.<\/li>\r\n \t<li>If the exponent is negative, move the decimal point \\(|n|\\) places to the left.<\/li>\r\n<\/ul>\r\n<\/li>\r\n \t<li>Check<\/li>\r\n<\/ol>\r\n<\/li>\r\n<\/ul>\r\n<h1>Practice Makes Perfect<\/h1>\r\n<h2 id=\"fs-id1169597742555\" style=\"text-align: left\">Use the Definition of a Negative Exponent<\/h2>\r\nIn the following exercises, simplify.\r\n<table style=\"border-collapse: collapse;width: 100%\" border=\"0\">\r\n<tbody>\r\n<tr>\r\n<td style=\"width: 50.0893%\">\r\n<p id=\"fs-id1169597740962\">1. a) \\({3}^{-4}\\) b) \\({10}^{-2}\\)<\/p>\r\n<\/td>\r\n<td style=\"width: 49.9107%\">\r\n<p id=\"fs-id1169597742567\">2. a) \\({4}^{-2}\\) b) \\({10}^{-3}\\)<\/p>\r\n<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 50.0893%\">\r\n<p id=\"fs-id1169597506410\">3. a) \\({2}^{-8}\\) b) \\({10}^{-2}\\)<\/p>\r\n<\/td>\r\n<td style=\"width: 49.9107%\">4. a) \\({5}^{-3}\\) b) \\({10}^{-5}\\)<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 50.0893%\">\r\n<p id=\"fs-id1169597741229\">5. a) \\(\\frac{1}{{c}^{-5}}\\) b) \\(\\frac{1}{{5}^{-2}}\\)<\/p>\r\n<\/td>\r\n<td style=\"width: 49.9107%\">\r\n<p id=\"fs-id1169597741177\">6. a) \\(\\frac{1}{{c}^{-5}}\\) b) \\(\\frac{1}{{3}^{-2}}\\)<\/p>\r\n<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 50.0893%\">\r\n<p id=\"fs-id1169597479428\">7. a) \\(\\frac{1}{{t}^{-9}}\\) b) \\(\\frac{1}{{10}^{-4}}\\)<\/p>\r\n<\/td>\r\n<td style=\"width: 49.9107%\">\r\n<p id=\"fs-id1169597479374\">8. a) \\(\\frac{1}{{q}^{-10}}\\) b) \\(\\frac{1}{{10}^{-3}}\\)<\/p>\r\n<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 50.0893%\">\r\n<p id=\"fs-id1169597690713\">9. a) \\({\\left(\\frac{3}{10}\\right)}^{-2}\\) b) \\({\\left(-\\frac{2}{cd}\\right)}^{-3}\\)<\/p>\r\n<\/td>\r\n<td style=\"width: 49.9107%\">\r\n<p id=\"fs-id1169597539677\">10. a) \\({\\left(\\frac{5}{8}\\right)}^{-2}\\) b) \\({\\left(-\\frac{3m}{n}\\right)}^{-2}\\)<\/p>\r\n<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 50.0893%\">\r\n<p id=\"fs-id1169597741526\">11. a)\\({\\left(\\frac{7}{2}\\right)}^{-3}\\) b)\\({\\left(-\\frac{3}{x{y}^{2}}\\right)}^{-3}\\)<\/p>\r\n<\/td>\r\n<td style=\"width: 49.9107%\">\r\n<p id=\"fs-id1169597741067\">12. a) \\({\\left(\\frac{4}{9}\\right)}^{-3}\\) b) \\({\\left(-\\frac{{u}^{2}}{2v}\\right)}^{-5}\\)<\/p>\r\n<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 50.0893%\">\r\n<p id=\"fs-id1169597702927\">13.<\/p>\r\na) \\({\\left(-7\\right)}^{-2}\\)\r\nb) \\(-{7}^{-2}\\)\r\nc) \\({\\left(-\\frac{1}{7}\\right)}^{-2}\\)\r\nd) \\(-{\\left(\\frac{1}{7}\\right)}^{-2}\\)<\/td>\r\n<td style=\"width: 49.9107%\">\r\n<p id=\"fs-id1169597741326\">14.<\/p>\r\na) \\({\\left(-5\\right)}^{-2}\\)\r\nb) \\(-{5}^{-2}\\)\r\nc) \\({\\left(-\\frac{1}{5}\\right)}^{-2}\\)\r\nd) \\(-{\\left(\\frac{1}{5}\\right)}^{-2}\\)<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 50.0893%\">\r\n<p id=\"fs-id1169597740612\">15.<\/p>\r\na) \\(-{5}^{-3}\\)\r\nb) \\({\\left(-\\frac{1}{5}\\right)}^{-3}\\)\r\nc) \\(-{\\left(\\frac{1}{5}\\right)}^{-3}\\)\r\nd) \\({\\left(-5\\right)}^{-3}\\)<\/td>\r\n<td style=\"width: 49.9107%\">\r\n<p id=\"fs-id1169597742731\">16.<\/p>\r\na) \\(-{3}^{-3}\\)\r\nb) \\({\\left(-\\frac{1}{3}\\right)}^{-3}\\)\r\nc) \\({\\left(\\frac{1}{3}\\right)}^{-3}\\)\r\nd) \\({\\left(-3\\right)}^{-3}\\)<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 50.0893%\">\r\n<p id=\"fs-id1169597518163\">17. a) \\(2\\cdot{5}^{-1}\\) b) \\({\\left(2\\cdot 5\\right)}^{-1}\\)<\/p>\r\n<\/td>\r\n<td style=\"width: 49.9107%\">\r\n<p id=\"fs-id1169597518095\">18. a) \\(3\\cdot{5}^{-1}\\) b) \\({\\left(3\\cdot 5\\right)}^{-1}\\)<\/p>\r\n<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 50.0893%\">\r\n<p id=\"fs-id1169597517274\">19. a) \\(3\\cdot{4}^{-2}\\) b) \\({\\left(3\\cdot 4\\right)}^{-2}\\)<\/p>\r\n<\/td>\r\n<td style=\"width: 49.9107%\">\r\n<p id=\"fs-id1169597517205\">20. a) \\(4\\cdot{5}^{-2}\\) b) \\({\\left(4\\cdot 5\\right)}^{-2}\\)<\/p>\r\n<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 50.0893%\">\r\n<p id=\"fs-id1169597740316\">21. a) \\({b}^{-5}\\) b) \\({\\left({k}^{2}\\right)}^{-5}\\)<\/p>\r\n<\/td>\r\n<td style=\"width: 49.9107%\">22. a) \\({m}^{-4}\\) b) \\({\\left({x}^{3}\\right)}^{-4}\\)<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 50.0893%\">\r\n<p id=\"fs-id1169597742888\">23. a) \\({s}^{-8}\\) b) \\({\\left({a}^{9}\\right)}^{-10}\\)<\/p>\r\n<\/td>\r\n<td style=\"width: 49.9107%\">24. a) \\({p}^{-10}\\) b) \\({\\left({q}^{6}\\right)}^{-8}\\)<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 50.0893%\">\r\n<p id=\"fs-id1169597742094\">25.<\/p>\r\na) \\(6{r}^{-1}\\)\r\nb) \\({\\left(6r\\right)}^{-1}\\)\r\nc) \\({\\left(-6r\\right)}^{-1}\\)<\/td>\r\n<td style=\"width: 49.9107%\">\r\n<p id=\"fs-id1169597742959\">26.<\/p>\r\na) \\(7{n}^{-1}\\)\r\nb) \\({\\left(7n\\right)}^{-1}\\)\r\nc) \\({\\left(-7n\\right)}^{-1}\\)<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 50.0893%\">\r\n<p id=\"fs-id1169597703627\">27.<\/p>\r\na) \\({\\left(2q\\right)}^{-4}\\)\r\nb) \\(2{q}^{-4}\\)\r\nc) \\(-2{q}^{-4}\\)<\/td>\r\n<td style=\"width: 49.9107%\">\r\n<p id=\"fs-id1169597441155\">28.<\/p>\r\na) \\({\\left(3p\\right)}^{-2}\\)\r\nb) \\(3{p}^{-2}\\)\r\nc) \\(-3{p}^{-2}\\)<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<h2 id=\"fs-id1169597740795\" style=\"text-align: left\">Simplify Expressions with Integer Exponents<\/h2>\r\nIn the following exercises, simplify.\r\n<table style=\"border-collapse: collapse;width: 100%;height: 293px\" border=\"0\">\r\n<tbody>\r\n<tr style=\"height: 94px\">\r\n<td style=\"width: 50%;height: 94px\">\r\n<p id=\"fs-id1169597740903\">29.<\/p>\r\na) \\({s}^{3}\\cdot{s}^{-7}\\)\r\nb) \\({q}^{-8}\\cdot{q}^{3}\\)\r\nc) \\({y}^{-2}\\cdot{y}^{-5}\\)<\/td>\r\n<td style=\"width: 50%;height: 94px\">30.\r\n\r\na) \\({b}^{4}{b}^{-8}\\)\r\nb) \\({r}^{-2}{r}^{5}\\)\r\nc) \\({x}^{-7}{x}^{-3}\\)<\/td>\r\n<\/tr>\r\n<tr style=\"height: 94px\">\r\n<td style=\"width: 50%;height: 94px\">\r\n<p id=\"fs-id1169597740082\">31.<\/p>\r\na) \\({y}^{5}\\cdot{y}^{-5}\\)\r\nb) \\(y\\cdot{y}^{5}\\)\r\nc) \\(y\\cdot{y}^{-5}\\)<\/td>\r\n<td style=\"width: 50%;height: 94px\">\r\n<p id=\"fs-id1169597701723\">32.<\/p>\r\na) \\({a}^{3}\\cdot{a}^{-3}\\)\r\nb) \\(a\\cdot{a}^{3}\\)\r\nc) \\(a\\cdot{a}^{-3}\\)<\/td>\r\n<\/tr>\r\n<tr style=\"height: 15px\">\r\n<td style=\"width: 50%;height: 15px\">33. \\({x}^{4}\\cdot{x}^{-2}\\cdot{x}^{-3}\\)<\/td>\r\n<td style=\"width: 50%;height: 15px\">34. \\(\\left({w}^{4}{x}^{-5}\\right)\\left({w}^{-2}{x}^{-4}\\right)\\)<\/td>\r\n<\/tr>\r\n<tr style=\"height: 15px\">\r\n<td style=\"width: 50%;height: 15px\">35. \\(\\left({m}^{3}{n}^{-3}\\right)\\left({m}^{-5}{n}^{-1}\\right)\\)<\/td>\r\n<td style=\"width: 50%;height: 15px\">36. \\(\\left(u{v}^{-2}\\right)\\left({u}^{-5}{v}^{-3}\\right)\\)<\/td>\r\n<\/tr>\r\n<tr style=\"height: 15px\">\r\n<td style=\"width: 50%;height: 15px\">37. \\(\\left(p{q}^{-4}\\right)\\left({p}^{-6}{q}^{-3}\\right)\\)<\/td>\r\n<td style=\"width: 50%;height: 15px\">38. \\(\\left(-6{c}^{-3}{d}^{9}\\right)\\left(2{c}^{4}{d}^{-5}\\right)\\)<\/td>\r\n<\/tr>\r\n<tr style=\"height: 15px\">\r\n<td style=\"width: 50%;height: 15px\">39. \\(\\left(-2{j}^{-5}{k}^{8}\\right)\\left(7{j}^{2}{k}^{-3}\\right)\\)<\/td>\r\n<td style=\"width: 50%;height: 15px\">40. \\(\\left(-4{r}^{-2}{s}^{-8}\\right)\\left(9{r}^{4}{s}^{3}\\right)\\)<\/td>\r\n<\/tr>\r\n<tr style=\"height: 15px\">\r\n<td style=\"width: 50%;height: 15px\">41. \\(\\left(-5{m}^{4}{n}^{6}\\right)\\left(8{m}^{-5}{n}^{-3}\\right)\\)<\/td>\r\n<td style=\"width: 50%;height: 15px\">42. \\({\\left(5{x}^{2}\\right)}^{-2}\\)<\/td>\r\n<\/tr>\r\n<tr style=\"height: 15px\">\r\n<td style=\"width: 50%;height: 15px\">43. \\({\\left(4{y}^{3}\\right)}^{-3}\\)<\/td>\r\n<td style=\"width: 50%;height: 15px\">44. \\({\\left(3{z}^{-3}\\right)}^{2}\\)<\/td>\r\n<\/tr>\r\n<tr style=\"height: 15px\">\r\n<td style=\"width: 50%;height: 15px\">45. \\({\\left(2{p}^{-5}\\right)}^{2}\\)<\/td>\r\n<td style=\"width: 50%;height: 15px\">46. \\(\\frac{{t}^{9}}{{t}^{-3}}\\)<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 50%\">47. \\(\\frac{{n}^{5}}{{n}^{-2}}\\)<\/td>\r\n<td style=\"width: 50%\">48. \\(\\frac{{x}^{-7}}{{x}^{-3}}\\)<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 50%\">49. \\(\\frac{{y}^{-5}}{{y}^{-10}}\\)<\/td>\r\n<td style=\"width: 50%\"><\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<h2 id=\"fs-id1169597726176\" style=\"text-align: left\">Convert from Decimal Notation to Scientific Notation<\/h2>\r\n<p id=\"fs-id1168746687025\">In the following exercises, write each number in scientific notation.<\/p>\r\n\r\n<table style=\"border-collapse: collapse;width: 100%\" border=\"0\">\r\n<tbody>\r\n<tr>\r\n<td style=\"width: 50%\">50. 57,000<\/td>\r\n<td style=\"width: 50%\">51. 340,000<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 50%\">52. 8,750,000<\/td>\r\n<td style=\"width: 50%\">53. 1,290,000<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 50%\">54. 0.026<\/td>\r\n<td style=\"width: 50%\">55. 0.041<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 50%\">56. 0.00000871<\/td>\r\n<td style=\"width: 50%\">57. 0.00000103<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<h2 id=\"fs-id1169597739266\" style=\"text-align: left\">Convert Scientific Notation to Decimal Form<\/h2>\r\n<p id=\"fs-id1168744093748\">In the following exercises, convert each number to decimal form.<\/p>\r\n\r\n<table style=\"border-collapse: collapse;width: 100%\" border=\"0\">\r\n<tbody>\r\n<tr>\r\n<td style=\"width: 50%\">58. \\(5.2\\phantom{\\rule{0.2em}{0ex}}\\times\\phantom{\\rule{0.2em}{0ex}}{10}^{2}\\)<\/td>\r\n<td style=\"width: 50%\">59. \\(8.3\\phantom{\\rule{0.2em}{0ex}}\\times\\phantom{\\rule{0.2em}{0ex}}{10}^{2}\\)<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 50%\">60. \\(7.5\\phantom{\\rule{0.2em}{0ex}}\\times\\phantom{\\rule{0.2em}{0ex}}{10}^{6}\\)<\/td>\r\n<td style=\"width: 50%\">61. \\(1.6\\phantom{\\rule{0.2em}{0ex}}\\times\\phantom{\\rule{0.2em}{0ex}}{10}^{10}\\)<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 50%\">62. \\(2.5\\phantom{\\rule{0.2em}{0ex}}\\times\\phantom{\\rule{0.2em}{0ex}}{10}^{-2}\\)<\/td>\r\n<td style=\"width: 50%\">63. \\(3.8\\phantom{\\rule{0.2em}{0ex}}\\times\\phantom{\\rule{0.2em}{0ex}}{10}^{-2}\\)<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 50%\">64. \\(4.13\\phantom{\\rule{0.2em}{0ex}}\\times\\phantom{\\rule{0.2em}{0ex}}{10}^{-5}\\)<\/td>\r\n<td style=\"width: 50%\">65. \\(1.93\\phantom{\\rule{0.2em}{0ex}}\\times\\phantom{\\rule{0.2em}{0ex}}{10}^{-5}\\)<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<h2 id=\"fs-id1169597702129\" style=\"text-align: left\">Multiply and Divide Using Scientific Notation<\/h2>\r\n<p id=\"fs-id1168746297450\">In the following exercises, multiply. Write your answer in decimal form.<\/p>\r\n\r\n<table style=\"border-collapse: collapse;width: 100%\" border=\"0\">\r\n<tbody>\r\n<tr>\r\n<td style=\"width: 50%\">66. \\(\\left(3\\phantom{\\rule{0.2em}{0ex}}\\times\\phantom{\\rule{0.2em}{0ex}}{10}^{-5}\\right)\\left(3\\phantom{\\rule{0.2em}{0ex}}\\times\\phantom{\\rule{0.2em}{0ex}}{10}^{9}\\right)\\)<\/td>\r\n<td style=\"width: 50%\">67. \\(\\left(2\\phantom{\\rule{0.2em}{0ex}}\\times\\phantom{\\rule{0.2em}{0ex}}{10}^{2}\\right)\\left(1\\phantom{\\rule{0.2em}{0ex}}\\times\\phantom{\\rule{0.2em}{0ex}}{10}^{-4}\\right)\\)<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 50%\">68. \\(\\left(7.1\\phantom{\\rule{0.2em}{0ex}}\\times\\phantom{\\rule{0.2em}{0ex}}{10}^{-2}\\right)\\left(2.4\\phantom{\\rule{0.2em}{0ex}}\\times\\phantom{\\rule{0.2em}{0ex}}{10}^{-4}\\right)\\)<\/td>\r\n<td style=\"width: 50%\">69. \\(\\left(3.5\\phantom{\\rule{0.2em}{0ex}}\\times\\phantom{\\rule{0.2em}{0ex}}{10}^{-4}\\right)\\left(1.6\\phantom{\\rule{0.2em}{0ex}}\\times\\phantom{\\rule{0.2em}{0ex}}{10}^{-2}\\right)\\)<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<p id=\"fs-id1169597537502\">In the following exercises, divide. Write your answer in decimal form.<\/p>\r\n\r\n<table style=\"border-collapse: collapse;width: 100%\" border=\"0\">\r\n<tbody>\r\n<tr>\r\n<td style=\"width: 50%\">70. \\(\\frac{7\\phantom{\\rule{0.2em}{0ex}}\\times\\phantom{\\rule{0.2em}{0ex}}{10}^{-3}}{1\\phantom{\\rule{0.2em}{0ex}}\\times\\phantom{\\rule{0.2em}{0ex}}{10}^{-7}}\\)<\/td>\r\n<td style=\"width: 50%\">71. \\(\\frac{5\\phantom{\\rule{0.2em}{0ex}}\\times\\phantom{\\rule{0.2em}{0ex}}{10}^{-2}}{1\\phantom{\\rule{0.2em}{0ex}}\\times\\phantom{\\rule{0.2em}{0ex}}{10}^{-10}}\\)<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 50%\">72. \\(\\frac{6\\phantom{\\rule{0.2em}{0ex}}\\times\\phantom{\\rule{0.2em}{0ex}}{10}^{4}}{3\\phantom{\\rule{0.2em}{0ex}}\\times\\phantom{\\rule{0.2em}{0ex}}{10}^{-2}}\\)<\/td>\r\n<td style=\"width: 50%\">73. \\(\\frac{8\\phantom{\\rule{0.2em}{0ex}}\\times\\phantom{\\rule{0.2em}{0ex}}{10}^{6}}{4\\phantom{\\rule{0.2em}{0ex}}\\times\\phantom{\\rule{0.2em}{0ex}}{10}^{-1}}\\)<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<h2 style=\"text-align: left\" data-type=\"title\">Everyday Math<\/h2>\r\n<table style=\"border-collapse: collapse;width: 100%\" border=\"0\">\r\n<tbody>\r\n<tr>\r\n<td style=\"width: 50%\">74. The population of the United States on July 1, 2010 was about 34,000,000. Write the number in scientific notation.<\/td>\r\n<td style=\"width: 50%\">75. The population of the world on July 1, 2010 was more than 6,850,000,000. Write the number in scientific notation<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 50%\">76. The average width of a human hair is 0.0018 centimetres. Write the number in scientific notation.<\/td>\r\n<td style=\"width: 50%\">77. The probability of winning the 2010 Megamillions lottery was about 0.0000000057. Write the number in scientific notation.<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 50%\">78. In 2010, the number of Facebook users each day who changed their status to \u2018engaged\u2019 was \\(2\\phantom{\\rule{0.2em}{0ex}}\\times\\phantom{\\rule{0.2em}{0ex}}{10}^{4}\\). Convert this number to decimal form.<\/td>\r\n<td style=\"width: 50%\">79. At the start of 2012, the US federal budget had a deficit of more than \\(\\text{?}1.5\\phantom{\\rule{0.2em}{0ex}}\\times\\phantom{\\rule{0.2em}{0ex}}{10}^{13}\\). Convert this number to decimal form.<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 50%\">80. The concentration of carbon dioxide in the atmosphere is \\(3.9\\phantom{\\rule{0.2em}{0ex}}\\times\\phantom{\\rule{0.2em}{0ex}}{10}^{-4}\\). Convert this number to decimal form.<\/td>\r\n<td style=\"width: 50%\">81. The width of a proton is \\(1\\phantom{\\rule{0.2em}{0ex}}\\times\\phantom{\\rule{0.2em}{0ex}}{10}^{-5}\\) of the width of an atom. Convert this number to decimal form.<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 50%\">\r\n<p id=\"fs-id1169597700250\">82. <strong data-effect=\"bold\">Health care costs<\/strong> The Centers for Medicare and Medicaid projects that American consumers will spend more than \\$4 trillion on health care by 2017<\/p>\r\n\r\n<ol id=\"fs-id1168746422024\" class=\"circled\" type=\"a\">\r\n \t<li>Write 4 trillion in decimal notation.<\/li>\r\n \t<li>Write 4 trillion in scientific notation.<\/li>\r\n<\/ol>\r\n<\/td>\r\n<td style=\"width: 50%\">83. <strong data-effect=\"bold\">Coin production<\/strong> In 1942, the U.S. Mint produced 154,500,000 nickels. Write 154,500,000 in scientific notation.<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 50%\">\r\n<p id=\"fs-id1169597704448\">84.<strong data-effect=\"bold\"> Distance<\/strong> The distance between Earth and one of the brightest stars in the night star is 33.7 light years. One light year is about 6,000,000,000,000 (6 trillion), miles.<\/p>\r\na) Write the number of miles in one light year in scientific notation.\r\n\r\nb)Use scientific notation to find the distance between Earth and the star in miles. Write the answer in scientific notation.<\/td>\r\n<td style=\"width: 50%\">\r\n<p id=\"fs-id1169597704506\">85. <strong data-effect=\"bold\">Debt<\/strong> At the end of fiscal year 2019 the gross Canadian federal government debt was estimated to be approximately \\$685,450,000,000 (\\$685.45 billion), according to the Federal Budget. The population of Canada was approximately 37,590,000 people at the end of fiscal year 2019<\/p>\r\na) Write the debt in scientific notation.\r\n\r\nb) Write the population in scientific notation.\r\n\r\nc) Find the amount of debt per person by using scientific notation to divide the debt by the population. Write the answer in scientific notation.<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<h2 style=\"text-align: left\" data-type=\"title\">Writing Exercises.<\/h2>\r\n<table style=\"border-collapse: collapse;width: 100%\" border=\"0\">\r\n<tbody>\r\n<tr>\r\n<td style=\"width: 50%\">86.\r\n\r\na) Explain the meaning of the exponent in the expression \\({2}^{3}\\).\r\n\r\nb) Explain the meaning of the exponent in the expression \\({2}^{-3}\\).<\/td>\r\n<td style=\"width: 50%\">87. When you convert a number from decimal notation to scientific notation, how do you know if the exponent will be positive or negative?<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<h1>Answers<\/h1>\r\n<table style=\"border-collapse: collapse;width: 100%;height: 255px\" border=\"0\">\r\n<tbody>\r\n<tr style=\"height: 17px\">\r\n<td style=\"width: 33.3333%;height: 17px\">1. a) \\(\\frac{1}{81}\\) b) \\(\\frac{1}{100}\\)<\/td>\r\n<td style=\"width: 33.3333%;height: 17px\">3. a) \\(\\frac{1}{256}\\) b) \\(\\frac{1}{100}\\)<\/td>\r\n<td style=\"width: 33.3333%;height: 17px\">5. a) \\({c}^{5}\\) b) 25<\/td>\r\n<\/tr>\r\n<tr style=\"height: 17px\">\r\n<td style=\"width: 33.3333%;height: 17px\">7. a) \\({t}^{9}\\) b) 10000<\/td>\r\n<td style=\"width: 33.3333%;height: 17px\">9. a) \\(\\frac{100}{9}\\) b) \\(-\\frac{{c}^{3}{d}^{3}}{8}\\)<\/td>\r\n<td style=\"width: 33.3333%;height: 17px\">11. a) \\(\\frac{8}{343}\\) b) \\(-\\frac{{x}^{3}{y}^{6}}{27}\\)<\/td>\r\n<\/tr>\r\n<tr style=\"height: 17px\">\r\n<td style=\"width: 33.3333%;height: 17px\">13. a) \\(\\frac{1}{49}\\) b) \\(-\\frac{1}{49}\\)c) 49 d) \\(-49\\)<\/td>\r\n<td style=\"width: 33.3333%;height: 17px\">15. a) \\(-\\frac{1}{125}\\) b) \\(-125\\) c) \\(-125\\)d)\\(-\\frac{1}{125}\\)<\/td>\r\n<td style=\"width: 33.3333%;height: 17px\">17. a) \\(\\frac{2}{5}\\) b) \\(\\frac{1}{10}\\)<\/td>\r\n<\/tr>\r\n<tr style=\"height: 17px\">\r\n<td style=\"width: 33.3333%;height: 17px\">19. a) \\(\\frac{3}{16}\\) b) \\(\\frac{1}{144}\\)<\/td>\r\n<td style=\"width: 33.3333%;height: 17px\">21. a)\\(\\frac{1}{{b}^{5}}\\) b) \\(\\frac{1}{{k}^{10}}\\)<\/td>\r\n<td style=\"width: 33.3333%;height: 17px\">23. a) \\(\\frac{1}{{s}^{8}}\\) b) \\(\\frac{1}{{a}^{90}}\\)<\/td>\r\n<\/tr>\r\n<tr style=\"height: 17px\">\r\n<td style=\"width: 33.3333%;height: 17px\">25. a) \\(\\frac{6}{r}\\) b) \\(\\frac{1}{6r}\\)c)\\(-\\frac{1}{6r}\\)<\/td>\r\n<td style=\"width: 33.3333%;height: 17px\">27. a)\\(\\frac{1}{16{q}^{4}}\\) b) \\(\\frac{2}{{q}^{4}}\\) c) \\(-\\frac{2}{{q}^{4}}\\)<\/td>\r\n<td style=\"width: 33.3333%;height: 17px\">29. a) \\(\\frac{1}{{s}^{4}}\\) b) \\(\\frac{1}{{q}^{5}}\\) c) \\(\\frac{1}{{y}^{7}}\\)<\/td>\r\n<\/tr>\r\n<tr style=\"height: 17px\">\r\n<td style=\"width: 33.3333%;height: 17px\">31. a) 1 b) \\({y}^{6}\\) c) \\(\\frac{1}{{y}^{4}}\\)<\/td>\r\n<td style=\"width: 33.3333%;height: 17px\">33. \\(\\frac{1}{x}\\)<\/td>\r\n<td style=\"width: 33.3333%;height: 17px\">35. \\(\\frac{1}{{m}^{2}{n}^{4}}\\)<\/td>\r\n<\/tr>\r\n<tr style=\"height: 17px\">\r\n<td style=\"width: 33.3333%;height: 17px\">37. \\(\\frac{1}{{p}^{5}{q}^{7}}\\)<\/td>\r\n<td style=\"width: 33.3333%;height: 17px\">39. \\(-\\frac{14{k}^{5}}{{j}^{3}}\\)<\/td>\r\n<td style=\"width: 33.3333%;height: 17px\">41. \\(-\\frac{40{n}^{3}}{m}\\)<\/td>\r\n<\/tr>\r\n<tr style=\"height: 17px\">\r\n<td style=\"width: 33.3333%;height: 17px\">43. \\(\\frac{1}{64{y}^{9}}\\)<\/td>\r\n<td style=\"width: 33.3333%;height: 17px\">45. \\(\\frac{4}{{p}^{10}}\\)<\/td>\r\n<td style=\"width: 33.3333%;height: 17px\">47. \\({n}^{7}\\)<\/td>\r\n<\/tr>\r\n<tr style=\"height: 17px\">\r\n<td style=\"width: 33.3333%;height: 17px\">49. \\({y}^{5}\\)<\/td>\r\n<td style=\"width: 33.3333%;height: 17px\">51. \\(3.4\\phantom{\\rule{0.2em}{0ex}}\\times\\phantom{\\rule{0.2em}{0ex}}{10}^{5}\\)<\/td>\r\n<td style=\"width: 33.3333%;height: 17px\">53. \\(1.29\\phantom{\\rule{0.2em}{0ex}}\\times\\phantom{\\rule{0.2em}{0ex}}{10}^{6}\\)<\/td>\r\n<\/tr>\r\n<tr style=\"height: 17px\">\r\n<td style=\"width: 33.3333%;height: 17px\">55. \\(4.1\\phantom{\\rule{0.2em}{0ex}}\\times\\phantom{\\rule{0.2em}{0ex}}{10}^{-2}\\)<\/td>\r\n<td style=\"width: 33.3333%;height: 17px\">57. \\(1.03\\phantom{\\rule{0.2em}{0ex}}\\times\\phantom{\\rule{0.2em}{0ex}}{10}^{-6}\\)<\/td>\r\n<td style=\"width: 33.3333%;height: 17px\">59. 830<\/td>\r\n<\/tr>\r\n<tr style=\"height: 17px\">\r\n<td style=\"width: 33.3333%;height: 17px\">61. 16,000,000,000<\/td>\r\n<td style=\"width: 33.3333%;height: 17px\">63. 0.038<\/td>\r\n<td style=\"width: 33.3333%;height: 17px\">65. 0.0000193<\/td>\r\n<\/tr>\r\n<tr style=\"height: 17px\">\r\n<td style=\"width: 33.3333%;height: 17px\">67. 0.02<\/td>\r\n<td style=\"width: 33.3333%;height: 17px\">69. \\(5.6\\phantom{\\rule{0.2em}{0ex}}\\times\\phantom{\\rule{0.2em}{0ex}}{10}^{-6}\\)<\/td>\r\n<td style=\"width: 33.3333%;height: 17px\">71. 500,000,000<\/td>\r\n<\/tr>\r\n<tr style=\"height: 17px\">\r\n<td style=\"width: 33.3333%;height: 17px\">73. 20,000,000<\/td>\r\n<td style=\"width: 33.3333%;height: 17px\">75. \\(6.85\\phantom{\\rule{0.2em}{0ex}}\\times\\phantom{\\rule{0.2em}{0ex}}{10}^{9}\\).<\/td>\r\n<td style=\"width: 33.3333%;height: 17px\">77. \\(5.7\\phantom{\\rule{0.2em}{0ex}}\\times\\phantom{\\rule{0.2em}{0ex}}{10}^{-9}\\)<\/td>\r\n<\/tr>\r\n<tr style=\"height: 17px\">\r\n<td style=\"width: 33.3333%;height: 17px\">79. 15,000,000,000,000<\/td>\r\n<td style=\"width: 33.3333%;height: 17px\">81. 0.00001<\/td>\r\n<td style=\"width: 33.3333%;height: 17px\">83. \\(1.545\\phantom{\\rule{0.2em}{0ex}}\\times\\phantom{\\rule{0.2em}{0ex}}{10}^{8}\\)<\/td>\r\n<\/tr>\r\n<tr style=\"height: 17px\">\r\n<td style=\"width: 33.3333%;height: 17px\" colspan=\"2\">85.\r\n<ol type=\"a\">\r\n \t<li>\\(6.8545\\phantom{\\rule{0.2em}{0ex}}\\times\\phantom{\\rule{0.2em}{0ex}}{10}^{11}\\)<\/li>\r\n \t<li>\\(3.759\\phantom{\\rule{0.2em}{0ex}}\\times\\phantom{\\rule{0.2em}{0ex}}{10}^{7}\\)<\/li>\r\n \t<li>\\(1.82349\\phantom{\\rule{0.2em}{0ex}}\\times\\phantom{\\rule{0.2em}{0ex}}{10}^{4}\\)<\/li>\r\n<\/ol>\r\n<\/td>\r\n<td style=\"width: 33.3333%;height: 17px\">87. Answers will vary<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<h1>Attributions<\/h1>\r\nThis chapter has been adapted from \u201cInteger Exponents and Scientific Notation\u201d in <a href=\"https:\/\/openstax.org\/details\/books\/elementary-algebra\"><em>Elementary Algebra<\/em> (OpenStax)<\/a> by Lynn Marecek and MaryAnne Anthony-Smith, which is under a <a href=\"https:\/\/creativecommons.org\/licenses\/by\/4.0\/\">CC BY 4.0 Licence<\/a>. Adapted by Izabela Mazur. See the Copyright page for more information.","rendered":"<div class=\"textbox textbox--learning-objectives\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">Learning Objectives<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<p>By the end of this section, you will be able to:<\/p>\n<ul>\n<li>Use the definition of a negative exponent<\/li>\n<li>Simplify expressions with integer exponents<\/li>\n<li>Convert from decimal notation to scientific notation<\/li>\n<li>Convert scientific notation to decimal form<\/li>\n<li>Multiply and divide using scientific notation<\/li>\n<\/ul>\n<\/div>\n<\/div>\n<h1>Use the Definition of a Negative Exponent<\/h1>\n<p id=\"fs-id1169597447461\">We saw that the Quotient Property for Exponents introduced earlier in this chapter, has two forms depending on whether the exponent is larger in the numerator or the denominator.<\/p>\n<div id=\"fs-id1169597539814\" data-type=\"note\">\n<div data-type=\"title\">\n<div class=\"textbox textbox--key-takeaways\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">Quotient Property for Exponents<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<p id=\"fs-id1169597504268\">If <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-3e9c4cc6ee8914c6fb4d5253abf7fc46_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#97;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"9\" style=\"vertical-align: 0px;\" \/> is a real number, <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-dfe13c0744369e0c0709de8599d9455f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#97;&#92;&#110;&#101;&#32;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"42\" style=\"vertical-align: -4px;\" \/>, and <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-8fe1b94dcc47778394ca62ab7c8655e0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#109;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#97;&#110;&#100;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#110;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"62\" style=\"vertical-align: -1px;\" \/> are whole numbers, then<\/p>\n<div data-type=\"equation\" data-label=\"\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-1605\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/uploads\/sites\/1441\/2021\/05\/Screenshot-2021-02-25-at-8.19.54-AM.png\" alt=\".\" width=\"379\" height=\"49\" \/><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<p id=\"fs-id1169597389005\">What if we just subtract exponents regardless of which is larger?<\/p>\n<p id=\"fs-id1169597579977\">Let\u2019s consider <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-2c2b218888377fcb0c74ab75ae61ac4a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#123;&#120;&#125;&#94;&#123;&#50;&#125;&#125;&#123;&#123;&#120;&#125;&#94;&#123;&#53;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"26\" width=\"15\" style=\"vertical-align: -7px;\" \/>.<\/p>\n<p>We subtract the exponent in the denominator from the exponent in the numerator.<\/p>\n<div class=\"unnumbered\" data-type=\"equation\" data-label=\"\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-62574287b033503f7c06f9942737c8f8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#98;&#101;&#103;&#105;&#110;&#123;&#97;&#114;&#114;&#97;&#121;&#125;&#123;&#99;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#102;&#114;&#97;&#99;&#123;&#123;&#120;&#125;&#94;&#123;&#50;&#125;&#125;&#123;&#123;&#120;&#125;&#94;&#123;&#53;&#125;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#92;&#32;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#123;&#120;&#125;&#94;&#123;&#50;&#45;&#53;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#92;&#32;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#123;&#120;&#125;&#94;&#123;&#45;&#51;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#101;&#110;&#100;&#123;&#97;&#114;&#114;&#97;&#121;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"62\" width=\"35\" style=\"vertical-align: -23px;\" \/><\/div>\n<p id=\"fs-id1169597492100\">We can also simplify <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-2c2b218888377fcb0c74ab75ae61ac4a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#123;&#120;&#125;&#94;&#123;&#50;&#125;&#125;&#123;&#123;&#120;&#125;&#94;&#123;&#53;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"26\" width=\"15\" style=\"vertical-align: -7px;\" \/> by dividing out common factors:<\/p>\n<p><span id=\"fs-id1169597389579\" data-type=\"media\" data-alt=\"Illustrated in this figure is x times x divided by x times x times x times x times x. Two xes cancel out in the numerator and denominator. Below this is the simplified term: 1 divided by x cubed.\"><img decoding=\"async\" class=\"aligncenter\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/uploads\/sites\/1441\/2021\/06\/CNX_ElemAlg_Figure_06_07_001_img_new.jpg\" alt=\"Illustrated in this figure is x times x divided by x times x times x times x times x. Two xes cancel out in the numerator and denominator. Below this is the simplified term: 1 divided by x cubed.\" data-media-type=\"image\/jpeg\" \/><\/span><\/p>\n<p id=\"fs-id1169597357807\">This implies that <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-b118f1c36b6f78ce43a7259e1819c89b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#120;&#125;&#94;&#123;&#45;&#51;&#125;&#61;&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#123;&#120;&#125;&#94;&#123;&#51;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"23\" width=\"69\" style=\"vertical-align: -7px;\" \/> and it leads us to the definition of a <em data-effect=\"italics\">negative exponent<\/em>.<\/p>\n<div id=\"fs-id1169597337099\" data-type=\"note\">\n<div data-type=\"title\">\n<div class=\"textbox textbox--key-takeaways\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">Negative Exponent<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<p>If <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-1772f700b10cd40d7410781794beb211_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#110;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"11\" style=\"vertical-align: 0px;\" \/> is an integer and <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-dfe13c0744369e0c0709de8599d9455f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#97;&#92;&#110;&#101;&#32;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"42\" style=\"vertical-align: -4px;\" \/>, then <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-2e4ab25b3a2e5c55ac5d165362a31987_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#97;&#125;&#94;&#123;&#45;&#110;&#125;&#61;&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#123;&#97;&#125;&#94;&#123;&#110;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"71\" style=\"vertical-align: -6px;\" \/>.<\/p>\n<\/div>\n<\/div>\n<p>&nbsp;<\/p>\n<\/div>\n<\/div>\n<p id=\"fs-id1169597576960\">The <span class=\"no-emphasis\" data-type=\"term\">negative exponent<\/span> tells us we can re-write the expression by taking the reciprocal of the base and then changing the sign of the exponent.<\/p>\n<p id=\"fs-id1169597478894\">Any expression that has negative exponents is not considered to be in simplest form. We will use the definition of a <span class=\"no-emphasis\" data-type=\"term\">negative exponent<\/span> and other properties of exponents to write the expression with only positive exponents.<\/p>\n<p id=\"fs-id1169597502645\">For example, if after simplifying an expression we end up with the expression <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-afdd8e333e03241d6b09dd8819d23672_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#120;&#125;&#94;&#123;&#45;&#51;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"28\" style=\"vertical-align: 0px;\" \/>, we will take one more step and write <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-2191fe1ed8365276d595df3327559941_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#123;&#120;&#125;&#94;&#123;&#51;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"23\" width=\"15\" style=\"vertical-align: -7px;\" \/>. The answer is considered to be in simplest form when it has only positive exponents.<\/p>\n<div class=\"textbox textbox--examples\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 1<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169597358215\" data-type=\"problem\">\n<p id=\"fs-id1169597383767\">Simplify: a) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-fa167090672f90743483dacbbdd005dc_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#52;&#125;&#94;&#123;&#45;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"27\" style=\"vertical-align: 0px;\" \/> b) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-eb0b6fc3c0e60a23266c29ed497c4f38_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#49;&#48;&#125;&#94;&#123;&#45;&#51;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"35\" style=\"vertical-align: 0px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1169597393699\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<table id=\"eip-426\" class=\"unnumbered unstyled\" summary=\".\">\n<tbody>\n<tr>\n<td>a)<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-fa167090672f90743483dacbbdd005dc_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#52;&#125;&#94;&#123;&#45;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"27\" style=\"vertical-align: 0px;\" \/><\/td>\n<\/tr>\n<tr>\n<td>Use the definition of a negative exponent, <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-2e4ab25b3a2e5c55ac5d165362a31987_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#97;&#125;&#94;&#123;&#45;&#110;&#125;&#61;&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#123;&#97;&#125;&#94;&#123;&#110;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"71\" style=\"vertical-align: -6px;\" \/>.<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-e043482892a7ca1f4ee06ed36daa84bc_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#123;&#52;&#125;&#94;&#123;&#50;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"23\" width=\"14\" style=\"vertical-align: -7px;\" \/><\/td>\n<\/tr>\n<tr>\n<td>Simplify.<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-fab031c2100c8a3af6c1a331735703f7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#49;&#54;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"14\" style=\"vertical-align: -6px;\" \/><\/td>\n<\/tr>\n<tr>\n<td>b)<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-eb0b6fc3c0e60a23266c29ed497c4f38_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#49;&#48;&#125;&#94;&#123;&#45;&#51;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"35\" style=\"vertical-align: 0px;\" \/><\/td>\n<\/tr>\n<tr>\n<td>Use the definition of a negative exponent, <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-2e4ab25b3a2e5c55ac5d165362a31987_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#97;&#125;&#94;&#123;&#45;&#110;&#125;&#61;&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#123;&#97;&#125;&#94;&#123;&#110;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"71\" style=\"vertical-align: -6px;\" \/>.<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-d68665835a0fb6e089587d1b51f4d24b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#123;&#49;&#48;&#125;&#94;&#123;&#51;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"23\" width=\"21\" style=\"vertical-align: -7px;\" \/><\/td>\n<\/tr>\n<tr>\n<td>Simplify.<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-ab883dcad349695f07b1a68a20b2cf3b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#49;&#48;&#48;&#48;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"28\" style=\"vertical-align: -6px;\" \/><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 1.1<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169597534816\" data-type=\"problem\">\n<p id=\"fs-id1169597341315\">Simplify: a) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-ebd0c4a7d3fbf67866f17a6f8e086435_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#50;&#125;&#94;&#123;&#45;&#51;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"27\" style=\"vertical-align: 0px;\" \/> b) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-865f81e2d79772d4508974d96ac86fdd_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#49;&#48;&#125;&#94;&#123;&#45;&#55;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"35\" style=\"vertical-align: 0px;\" \/>.<\/p>\n<\/div>\n<div data-type=\"solution\">\n<details>\n<summary>Show answer<\/summary>\n<p id=\"fs-id1169597541824\">a) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-c2cfa6670ebdcbfaa8e068cc03a9a346_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#56;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"7\" style=\"vertical-align: -6px;\" \/> b) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-302346007f9b84bb5f40e70f49827a71_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#123;&#49;&#48;&#125;&#94;&#123;&#55;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"23\" width=\"21\" style=\"vertical-align: -7px;\" \/><\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1169597511869\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1169597441593\" data-type=\"exercise\">\n<div id=\"fs-id1169597534816\" data-type=\"problem\">\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 1.2<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169597351516\" data-type=\"problem\">\n<p>Simplify: a) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-2c43fd80a498aad8c8dabf43c7e3eedd_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#51;&#125;&#94;&#123;&#45;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"27\" style=\"vertical-align: 0px;\" \/> b) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-78c90a7670dd413610ac83f3f58d5b15_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#49;&#48;&#125;&#94;&#123;&#45;&#52;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"35\" style=\"vertical-align: 0px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1169597500356\" data-type=\"solution\">\n<details>\n<summary>Show answer<\/summary>\n<p id=\"fs-id1169597411392\">a) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-1766124ef2f6618be83e77f1e9948915_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#57;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"7\" style=\"vertical-align: -6px;\" \/> b) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-e89edcb829352efa52d429225b175796_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#49;&#48;&#44;&#48;&#48;&#48;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"25\" width=\"39\" style=\"vertical-align: -9px;\" \/><\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<p id=\"fs-id1169597339847\">In <a class=\"autogenerated-content\" href=\"#fs-id1169597358215\">(Example 1)<\/a> we raised an integer to a negative exponent. What happens when we raise a fraction to a negative exponent? We\u2019ll start by looking at what happens to a fraction whose numerator is one and whose denominator is an integer raised to a negative exponent.<\/p>\n<table id=\"eip-532\" class=\"unnumbered unstyled\" summary=\".\">\n<tbody>\n<tr>\n<td><\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-5157085a33ec72660e782f46db8a4888_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#123;&#97;&#125;&#94;&#123;&#45;&#110;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"36\" width=\"30\" style=\"vertical-align: -12px;\" \/><\/td>\n<\/tr>\n<tr>\n<td>Use the definition of a negative exponent, <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-468d971c785ce51868beb94f91165f44_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#97;&#125;&#94;&#123;&#45;&#110;&#125;&#61;&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#123;&#97;&#125;&#94;&#123;&#110;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"36\" width=\"74\" style=\"vertical-align: -12px;\" \/>.<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-8258a89ab62fbb718979415555cdf780_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#92;&#99;&#111;&#108;&#111;&#114;&#123;&#114;&#101;&#100;&#125;&#123;&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#123;&#97;&#125;&#94;&#123;&#110;&#125;&#125;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"43\" width=\"20\" style=\"vertical-align: -19px;\" \/><\/td>\n<\/tr>\n<tr>\n<td>Simplify the complex fraction.<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-fc7ae04ee38e99b816bd3709e0412794_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#92;&#99;&#100;&#111;&#116;&#92;&#102;&#114;&#97;&#99;&#123;&#123;&#97;&#125;&#94;&#123;&#110;&#125;&#125;&#123;&#49;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"23\" width=\"39\" style=\"vertical-align: -6px;\" \/><\/td>\n<\/tr>\n<tr>\n<td>Multiply.<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-2cfcfd3f416e85c67a85ce56c2939581_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#97;&#125;&#94;&#123;&#110;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"17\" style=\"vertical-align: 0px;\" \/><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p id=\"fs-id1169597484548\">This leads to the Property of Negative Exponents.<\/p>\n<div class=\"textbox textbox--key-takeaways\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">Property of Negative Exponents<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<p>If <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-1772f700b10cd40d7410781794beb211_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#110;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"11\" style=\"vertical-align: 0px;\" \/> is an integer and <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-dfe13c0744369e0c0709de8599d9455f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#97;&#92;&#110;&#101;&#32;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"42\" style=\"vertical-align: -4px;\" \/>, then <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-864534955e4c36701312e28be58fec05_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#123;&#97;&#125;&#94;&#123;&#45;&#110;&#125;&#125;&#61;&#123;&#97;&#125;&#94;&#123;&#110;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"23\" width=\"67\" style=\"vertical-align: -7px;\" \/>.<\/p>\n<\/div>\n<\/div>\n<div id=\"fs-id1169597577846\" data-type=\"note\">\n<div class=\"textbox textbox--examples\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 2<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169597529407\" data-type=\"problem\">\n<p>Simplify: a) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-6d0d6ffd1b1638fa454e0044fc335f0c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#123;&#121;&#125;&#94;&#123;&#45;&#52;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"26\" width=\"24\" style=\"vertical-align: -10px;\" \/> b) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-6089359a69d0de84bd70e6e5f4d138af_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#123;&#51;&#125;&#94;&#123;&#45;&#50;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"23\" width=\"23\" style=\"vertical-align: -7px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1169597395509\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<table id=\"eip-453\" class=\"unnumbered unstyled\" summary=\".\">\n<tbody>\n<tr>\n<td>a)<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-6d0d6ffd1b1638fa454e0044fc335f0c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#123;&#121;&#125;&#94;&#123;&#45;&#52;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"26\" width=\"24\" style=\"vertical-align: -10px;\" \/><\/td>\n<\/tr>\n<tr>\n<td>Use the property of a negative exponent, <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-864534955e4c36701312e28be58fec05_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#123;&#97;&#125;&#94;&#123;&#45;&#110;&#125;&#125;&#61;&#123;&#97;&#125;&#94;&#123;&#110;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"23\" width=\"67\" style=\"vertical-align: -7px;\" \/>.<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-846ba901de07c3d484ffe5f722307f8e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#121;&#125;&#94;&#123;&#52;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"16\" style=\"vertical-align: -4px;\" \/><\/td>\n<\/tr>\n<tr>\n<td>b)<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-6089359a69d0de84bd70e6e5f4d138af_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#123;&#51;&#125;&#94;&#123;&#45;&#50;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"23\" width=\"23\" style=\"vertical-align: -7px;\" \/><\/td>\n<\/tr>\n<tr>\n<td>Use the property of a negative exponent, <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-864534955e4c36701312e28be58fec05_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#123;&#97;&#125;&#94;&#123;&#45;&#110;&#125;&#125;&#61;&#123;&#97;&#125;&#94;&#123;&#110;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"23\" width=\"67\" style=\"vertical-align: -7px;\" \/>.<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-abc6b59f7724ef5781da724a40e52763_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#51;&#125;&#94;&#123;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"16\" style=\"vertical-align: 0px;\" \/><\/td>\n<\/tr>\n<tr>\n<td>Simplify.<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-169193ff8b4fc5625a37c03183cf5bf0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#57;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"9\" style=\"vertical-align: 0px;\" \/><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 2.1<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169597467255\" data-type=\"problem\">\n<p id=\"fs-id1169597527634\">Simplify: a) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-874d876fa457d7b4b3e45de61d4ca31a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#123;&#112;&#125;&#94;&#123;&#45;&#56;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"26\" width=\"25\" style=\"vertical-align: -10px;\" \/> b) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-1f31349bd988d3f9b49ebf3d1cc60875_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#123;&#52;&#125;&#94;&#123;&#45;&#51;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"23\" width=\"23\" style=\"vertical-align: -7px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1169597500869\" data-type=\"solution\">\n<details>\n<summary>Show answer<\/summary>\n<p id=\"fs-id1169597465620\">a) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-1bb22c9ae1d93bf0750aaa35b1e40999_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#112;&#125;&#94;&#123;&#56;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"17\" style=\"vertical-align: -4px;\" \/> b) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-b7bce2e66f4ed3aee3cebf33e0d35ec9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#54;&#52;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"18\" style=\"vertical-align: 0px;\" \/><\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1169597490680\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1169597430976\" data-type=\"exercise\">\n<div id=\"fs-id1169597500869\" data-type=\"solution\">\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 2.2<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169597444878\" data-type=\"problem\">\n<p id=\"fs-id1169597447912\">Simplify: a) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-ccfca1aee030889f44a930d555f26985_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#123;&#113;&#125;&#94;&#123;&#45;&#55;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"26\" width=\"23\" style=\"vertical-align: -10px;\" \/> b) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-09c9ad50e4968e2e95d45c2e25cae706_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#123;&#50;&#125;&#94;&#123;&#45;&#52;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"23\" width=\"23\" style=\"vertical-align: -7px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1169597510009\" data-type=\"solution\">\n<details>\n<summary>Show answer<\/summary>\n<p id=\"fs-id1169597350486\">a) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-13e091b32be4599e64fbaaaf70403d1f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#113;&#125;&#94;&#123;&#55;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"16\" style=\"vertical-align: -4px;\" \/> b) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-6e249588b998635f5e95a8679b5cf576_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#54;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"17\" style=\"vertical-align: 0px;\" \/><\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<p id=\"fs-id1169597393899\">Suppose now we have a fraction raised to a negative exponent. Let\u2019s use our definition of negative exponents to lead us to a new property.<\/p>\n<table id=\"eip-239\" summary=\".\">\n<tbody>\n<tr>\n<td><\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-6550b5f2303cb8c0c21fe40cc825e723_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#92;&#102;&#114;&#97;&#99;&#123;&#51;&#125;&#123;&#52;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#94;&#123;&#45;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"26\" width=\"43\" style=\"vertical-align: -7px;\" \/><\/td>\n<\/tr>\n<tr>\n<td>Use the definition of a negative exponent, <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-2e4ab25b3a2e5c55ac5d165362a31987_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#97;&#125;&#94;&#123;&#45;&#110;&#125;&#61;&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#123;&#97;&#125;&#94;&#123;&#110;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"71\" style=\"vertical-align: -6px;\" \/>.<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-bee7e4780534aae46a36cfa3426964f3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#92;&#102;&#114;&#97;&#99;&#123;&#51;&#125;&#123;&#52;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#94;&#123;&#50;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"33\" width=\"31\" style=\"vertical-align: -17px;\" \/><\/td>\n<\/tr>\n<tr>\n<td>Simplify the denominator.<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-fd20fbcc1963fdb539553b0463ef6b29_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#92;&#102;&#114;&#97;&#99;&#123;&#57;&#125;&#123;&#49;&#54;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"29\" width=\"16\" style=\"vertical-align: -13px;\" \/><\/td>\n<\/tr>\n<tr>\n<td>Simplify the complex fraction.<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-19fae62d0f3e25f059154c105daa8554_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#54;&#125;&#123;&#57;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"14\" style=\"vertical-align: -6px;\" \/><\/td>\n<\/tr>\n<tr>\n<td>But we know that <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-19fae62d0f3e25f059154c105daa8554_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#54;&#125;&#123;&#57;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"14\" style=\"vertical-align: -6px;\" \/> is <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-0c321fda8ae68a9bc0d8ff05b64071ad_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#92;&#102;&#114;&#97;&#99;&#123;&#52;&#125;&#123;&#51;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#94;&#123;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"26\" width=\"32\" style=\"vertical-align: -7px;\" \/>.<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>This tells us that:<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-3c4e41dda8997135e3bd1ed760e054a8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#92;&#102;&#114;&#97;&#99;&#123;&#51;&#125;&#123;&#52;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#94;&#123;&#45;&#50;&#125;&#61;&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#92;&#102;&#114;&#97;&#99;&#123;&#52;&#125;&#123;&#51;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#94;&#123;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"26\" width=\"101\" style=\"vertical-align: -7px;\" \/><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p id=\"fs-id1169597409988\">To get from the original fraction raised to a negative exponent to the final result, we took the reciprocal of the base\u2014the fraction\u2014and changed the sign of the exponent.<\/p>\n<p id=\"fs-id1169597515519\">This leads us to the <em data-effect=\"italics\">Quotient to a Negative Power Property<\/em>.<\/p>\n<div class=\"textbox textbox--key-takeaways\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">Quotient to a Negative Exponent Property<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<p>If <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-9bd295ba1eac106832650cda85daba43_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#97;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#97;&#110;&#100;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#98;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"53\" style=\"vertical-align: -1px;\" \/> are real numbers, <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-c0997299c1155dea7e6aa4b703e561cd_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#97;&#92;&#110;&#101;&#32;&#48;&#44;&#98;&#92;&#110;&#101;&#32;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"90\" style=\"vertical-align: -4px;\" \/>, and <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-1772f700b10cd40d7410781794beb211_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#110;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"11\" style=\"vertical-align: 0px;\" \/> is an integer, then <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-f03914d6346e9ed2526089212f9eeccd_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#92;&#102;&#114;&#97;&#99;&#123;&#97;&#125;&#123;&#98;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#94;&#123;&#45;&#110;&#125;&#61;&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#92;&#102;&#114;&#97;&#99;&#123;&#98;&#125;&#123;&#97;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#94;&#123;&#110;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"24\" width=\"104\" style=\"vertical-align: -7px;\" \/>.<\/p>\n<\/div>\n<\/div>\n<div id=\"fs-id1169597416290\" data-type=\"note\">\n<div class=\"textbox textbox--examples\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 3<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169597577456\" data-type=\"problem\">\n<p id=\"fs-id1169597492476\">Simplify: a) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-eab2a7399fdf05d6ff2060888a49629e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#92;&#102;&#114;&#97;&#99;&#123;&#53;&#125;&#123;&#55;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#94;&#123;&#45;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"26\" width=\"43\" style=\"vertical-align: -7px;\" \/> b) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-af659c177a00fd4068aa8426e7bd3fd2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#92;&#102;&#114;&#97;&#99;&#123;&#50;&#120;&#125;&#123;&#121;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#94;&#123;&#45;&#51;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"35\" width=\"68\" style=\"vertical-align: -11px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1169597580588\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<table id=\"eip-116\" class=\"unnumbered unstyled\" summary=\".\">\n<tbody>\n<tr>\n<td>a)<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-eab2a7399fdf05d6ff2060888a49629e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#92;&#102;&#114;&#97;&#99;&#123;&#53;&#125;&#123;&#55;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#94;&#123;&#45;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"26\" width=\"43\" style=\"vertical-align: -7px;\" \/><\/td>\n<\/tr>\n<tr>\n<td>Use the Quotient to a Negative Exponent Property, <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-f03914d6346e9ed2526089212f9eeccd_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#92;&#102;&#114;&#97;&#99;&#123;&#97;&#125;&#123;&#98;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#94;&#123;&#45;&#110;&#125;&#61;&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#92;&#102;&#114;&#97;&#99;&#123;&#98;&#125;&#123;&#97;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#94;&#123;&#110;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"24\" width=\"104\" style=\"vertical-align: -7px;\" \/>.<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>Take the reciprocal of the fraction and change the sign of the exponent.<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-3e9ad4cc53caba6909a68dbc5e98535c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#92;&#102;&#114;&#97;&#99;&#123;&#55;&#125;&#123;&#53;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#94;&#123;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"26\" width=\"32\" style=\"vertical-align: -7px;\" \/><\/td>\n<\/tr>\n<tr>\n<td>Simplify.<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-af1efaf88e550553f7aa6fc29f513f3b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#52;&#57;&#125;&#123;&#50;&#53;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"14\" style=\"vertical-align: -6px;\" \/><\/td>\n<\/tr>\n<tr>\n<td>b)<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-af659c177a00fd4068aa8426e7bd3fd2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#92;&#102;&#114;&#97;&#99;&#123;&#50;&#120;&#125;&#123;&#121;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#94;&#123;&#45;&#51;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"35\" width=\"68\" style=\"vertical-align: -11px;\" \/><\/td>\n<\/tr>\n<tr>\n<td>Use the Quotient to a Negative Exponent Property, <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-f03914d6346e9ed2526089212f9eeccd_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#92;&#102;&#114;&#97;&#99;&#123;&#97;&#125;&#123;&#98;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#94;&#123;&#45;&#110;&#125;&#61;&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#92;&#102;&#114;&#97;&#99;&#123;&#98;&#125;&#123;&#97;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#94;&#123;&#110;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"24\" width=\"104\" style=\"vertical-align: -7px;\" \/>.<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>Take the reciprocal of the fraction and change the sign of the exponent.<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-224cdeb7dca3a6f899db2ccc20ef5fef_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#92;&#102;&#114;&#97;&#99;&#123;&#121;&#125;&#123;&#50;&#120;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#94;&#123;&#51;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"26\" width=\"54\" style=\"vertical-align: -7px;\" \/><\/td>\n<\/tr>\n<tr>\n<td>Simplify.<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-bc877c6e2e40e7c253d9d3953b126617_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#92;&#102;&#114;&#97;&#99;&#123;&#123;&#121;&#125;&#94;&#123;&#51;&#125;&#125;&#123;&#56;&#123;&#120;&#125;&#94;&#123;&#51;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"27\" width=\"37\" style=\"vertical-align: -7px;\" \/><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 3.1<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169597520921\" data-type=\"problem\">\n<p id=\"fs-id1169597467530\">Simplify: a) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-bfd6c16a9458aa939e81ea9a6f231468_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#92;&#102;&#114;&#97;&#99;&#123;&#50;&#125;&#123;&#51;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#94;&#123;&#45;&#52;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"26\" width=\"43\" style=\"vertical-align: -7px;\" \/> b) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-8b01000bc91ebf6b30823caf51796a34_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#92;&#102;&#114;&#97;&#99;&#123;&#54;&#109;&#125;&#123;&#110;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#94;&#123;&#45;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"26\" width=\"69\" style=\"vertical-align: -7px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1169597540982\" data-type=\"solution\">\n<details>\n<summary>Show answer<\/summary>\n<p id=\"fs-id1169597507465\">a) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-a56a6fa7a11bcc9d0e71e6407f64dc0c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#56;&#49;&#125;&#123;&#49;&#54;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"14\" style=\"vertical-align: -6px;\" \/> b) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-e26878419892775f5c4d15589f840631_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#123;&#110;&#125;&#94;&#123;&#50;&#125;&#125;&#123;&#51;&#54;&#123;&#109;&#125;&#94;&#123;&#50;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"26\" width=\"33\" style=\"vertical-align: -7px;\" \/><\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1169597422172\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1169597533646\" data-type=\"exercise\">\n<div id=\"fs-id1169597540982\" data-type=\"solution\">\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 3.2<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div data-type=\"problem\">\n<p id=\"fs-id1169597702065\">Simplify: a) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-3a537ed46dfb2b4872bd61b574346cd1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#92;&#102;&#114;&#97;&#99;&#123;&#51;&#125;&#123;&#53;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#94;&#123;&#45;&#51;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"26\" width=\"43\" style=\"vertical-align: -7px;\" \/> b) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-9812b269da28f244cc0557874e449450_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#92;&#102;&#114;&#97;&#99;&#123;&#97;&#125;&#123;&#50;&#98;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#94;&#123;&#45;&#52;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"26\" width=\"63\" style=\"vertical-align: -7px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1169597415785\" data-type=\"solution\">\n<details>\n<summary>Show answer<\/summary>\n<p id=\"fs-id1169597500693\">a) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-95a48d8330e1a0e795d2b85af649ad81_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#50;&#53;&#125;&#123;&#50;&#55;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"21\" style=\"vertical-align: -6px;\" \/> b) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-0c3455301399095dac9286fd8960fcd3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#54;&#123;&#98;&#125;&#94;&#123;&#52;&#125;&#125;&#123;&#123;&#97;&#125;&#94;&#123;&#52;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"26\" width=\"27\" style=\"vertical-align: -7px;\" \/><\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<p>When simplifying an expression with exponents, we must be careful to correctly identify the base.<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--examples\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 4<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169597540378\" data-type=\"problem\">\n<p id=\"fs-id1169597703489\">Simplify: a) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-e9405603d71dd0dac7a26ddc62926c84_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#51;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#94;&#123;&#45;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"53\" style=\"vertical-align: -5px;\" \/> b) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-459b45bdaf549a7f05bfeb57b0933afc_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#123;&#51;&#125;&#94;&#123;&#45;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"40\" style=\"vertical-align: 0px;\" \/> c) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-2e39721280fb8634e7260bf65e45b34f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#51;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#94;&#123;&#45;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"26\" width=\"57\" style=\"vertical-align: -7px;\" \/> d) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-d58324a8fa4c5f494b34f75541773aca_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#51;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#94;&#123;&#45;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"26\" width=\"58\" style=\"vertical-align: -7px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1169597467914\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<table id=\"eip-407\" class=\"unnumbered unstyled\" summary=\".\">\n<tbody>\n<tr>\n<td>a) Here the exponent applies to the base <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-5cac4bc2f960e6a9754ddf4913c65741_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#51;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"22\" style=\"vertical-align: 0px;\" \/>.<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-e9405603d71dd0dac7a26ddc62926c84_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#51;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#94;&#123;&#45;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"53\" style=\"vertical-align: -5px;\" \/><\/td>\n<\/tr>\n<tr>\n<td>Take the reciprocal of the base and change the sign of the exponent.<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-880b2084c9f7895b498f9185482edd32_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#51;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#94;&#123;&#50;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"29\" width=\"36\" style=\"vertical-align: -13px;\" \/><\/td>\n<\/tr>\n<tr>\n<td>Simplify.<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-1766124ef2f6618be83e77f1e9948915_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#57;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"7\" style=\"vertical-align: -6px;\" \/><\/td>\n<\/tr>\n<tr>\n<td>b) The expression <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-459b45bdaf549a7f05bfeb57b0933afc_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#123;&#51;&#125;&#94;&#123;&#45;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"40\" style=\"vertical-align: 0px;\" \/> means &#8220;find the opposite of <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-2c43fd80a498aad8c8dabf43c7e3eedd_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#51;&#125;&#94;&#123;&#45;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"27\" style=\"vertical-align: 0px;\" \/>.&#8221; Here the exponent applies to the base <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-3e01b6d52674d4c8c5e7627d258a2586_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#51;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#94;&#123;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"23\" width=\"37\" style=\"vertical-align: -7px;\" \/>.<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-459b45bdaf549a7f05bfeb57b0933afc_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#123;&#51;&#125;&#94;&#123;&#45;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"40\" style=\"vertical-align: 0px;\" \/><\/td>\n<\/tr>\n<tr>\n<td>Rewrite as a product with <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-6d903871cc61f2b2aedacc7094bd5a1e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"21\" style=\"vertical-align: 0px;\" \/>.<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-46f6572c6940c9349afc90d8aed87165_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#49;&#92;&#99;&#100;&#111;&#116;&#123;&#51;&#125;&#94;&#123;&#45;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"61\" style=\"vertical-align: 0px;\" \/><\/td>\n<\/tr>\n<tr>\n<td>Take the reciprocal of the base and change the sign of the exponent.<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-bbce7aee0689d581971e68033e5b2f43_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#49;&#92;&#99;&#100;&#111;&#116;&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#123;&#51;&#125;&#94;&#123;&#50;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"23\" width=\"50\" style=\"vertical-align: -7px;\" \/><\/td>\n<\/tr>\n<tr>\n<td>Simplify.<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-399fd035bc791de46375c94b031c3400_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#57;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"22\" style=\"vertical-align: -6px;\" \/><\/td>\n<\/tr>\n<tr>\n<td>c) Here the exponent applies to the base <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-3e01b6d52674d4c8c5e7627d258a2586_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#51;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#94;&#123;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"23\" width=\"37\" style=\"vertical-align: -7px;\" \/>.<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-2e39721280fb8634e7260bf65e45b34f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#51;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#94;&#123;&#45;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"26\" width=\"57\" style=\"vertical-align: -7px;\" \/><\/td>\n<\/tr>\n<tr>\n<td>Take the reciprocal of the base and change the sign of the exponent.<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-57226e23bab1e11b6bf8f8eebe6e7b9d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#92;&#102;&#114;&#97;&#99;&#123;&#51;&#125;&#123;&#49;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#94;&#123;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"26\" width=\"46\" style=\"vertical-align: -7px;\" \/><\/td>\n<\/tr>\n<tr>\n<td>Simplify.<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-169193ff8b4fc5625a37c03183cf5bf0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#57;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"9\" style=\"vertical-align: 0px;\" \/><\/td>\n<\/tr>\n<tr>\n<td>d) The expression <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-d58324a8fa4c5f494b34f75541773aca_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#51;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#94;&#123;&#45;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"26\" width=\"58\" style=\"vertical-align: -7px;\" \/> means &#8220;find the opposite of <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-ed8a5b9d5fcb4d2c8c55292b84c02f36_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#51;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#94;&#123;&#45;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"26\" width=\"43\" style=\"vertical-align: -7px;\" \/>.&#8221; Here the exponent applies to the base <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-16207d4c55d8d7da0e138859d94cdc47_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#51;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"23\" width=\"23\" style=\"vertical-align: -7px;\" \/>.<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>Rewrite as a product with <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-6d903871cc61f2b2aedacc7094bd5a1e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"21\" style=\"vertical-align: 0px;\" \/>.<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-f52374e6ac4731d3ec08e52496550371_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#49;&#92;&#99;&#100;&#111;&#116;&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#51;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#94;&#123;&#45;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"26\" width=\"79\" style=\"vertical-align: -7px;\" \/><\/td>\n<\/tr>\n<tr>\n<td>Take the reciprocal of the base and change the sign of the exponent.<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-87387a75f760f87cd0f27ca8dd6f61c7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#49;&#92;&#99;&#100;&#111;&#116;&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#92;&#102;&#114;&#97;&#99;&#123;&#51;&#125;&#123;&#49;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#94;&#123;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"26\" width=\"68\" style=\"vertical-align: -7px;\" \/><\/td>\n<\/tr>\n<tr>\n<td>Simplify.<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-68ac888b00edd47ce83018453d555767_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#57;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"22\" style=\"vertical-align: 0px;\" \/><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 4.1<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169597457044\" data-type=\"problem\">\n<p id=\"fs-id1169597457046\">Simplify: a) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-543b6b927d60444409cb5a6aadbe8b55_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#53;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#94;&#123;&#45;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"53\" style=\"vertical-align: -5px;\" \/> b) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-135f5311f3f86fc939207ffa372eaf51_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#123;&#53;&#125;&#94;&#123;&#45;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"40\" style=\"vertical-align: 0px;\" \/> c) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-7b1dce0e48c52b7bc354cb8c0c735076_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#53;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#94;&#123;&#45;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"26\" width=\"57\" style=\"vertical-align: -7px;\" \/> d) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-8493b9625abd93b0482dbe719d7dd8ae_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#53;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#94;&#123;&#45;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"26\" width=\"58\" style=\"vertical-align: -7px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1169597577197\" data-type=\"solution\">\n<details>\n<summary>Show answer<\/summary>\n<p id=\"fs-id1169597577199\">a) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-f2396d0d5bba7b5b83a039a18ab38613_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#50;&#53;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"14\" style=\"vertical-align: -6px;\" \/> b) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-e18032a8cc48054b2faa13961b218673_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#50;&#53;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"29\" style=\"vertical-align: -6px;\" \/> c) 25 d) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-17249d3b93794980404be1b495e96dec_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#50;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"30\" style=\"vertical-align: 0px;\" \/><\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1169597741466\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1169597741469\" data-type=\"exercise\">\n<div id=\"fs-id1169597577197\" data-type=\"solution\">\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 4.2<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169597540994\" data-type=\"problem\">\n<p id=\"fs-id1169597540997\">Simplify: a) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-bf3c1fa27b7c255e41ce62d187af35dc_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#55;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#94;&#123;&#45;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"53\" style=\"vertical-align: -5px;\" \/> b) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-cc229a9cb246c7cc81b4fe66ce272ea5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#123;&#55;&#125;&#94;&#123;&#45;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"40\" style=\"vertical-align: 0px;\" \/>, c) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-571e0ab64342e9b566be3818f1ff9708_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#55;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#94;&#123;&#45;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"26\" width=\"57\" style=\"vertical-align: -7px;\" \/> d) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-1ffbb7774061cca34f8e3fa526260c22_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#55;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#94;&#123;&#45;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"26\" width=\"58\" style=\"vertical-align: -7px;\" \/>.<\/p>\n<\/div>\n<div data-type=\"solution\">\n<details>\n<summary>Show answer<\/summary>\n<p id=\"fs-id1169597483796\">a) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-ea2d1dcf02248d8daa27c15cd901d859_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#52;&#57;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"14\" style=\"vertical-align: -6px;\" \/> b) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-2fe70375c414a59c1fb292a62854cb03_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#52;&#57;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"29\" style=\"vertical-align: -6px;\" \/> c) 49 d) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-48b5f780791c20326d1316c7be569f56_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#52;&#57;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"31\" style=\"vertical-align: 0px;\" \/><\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<p id=\"fs-id1169597533353\">We must be careful to follow the Order of Operations. In the next example, parts (a) and (b) look similar, but the results are different.<\/p>\n<div class=\"textbox textbox--examples\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 5<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169597492583\" data-type=\"problem\">\n<p id=\"fs-id1169597492586\">Simplify: a) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-cc2b16c6b1626c739c80ba4aefc5f6fa_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#52;&#92;&#99;&#100;&#111;&#116;&#123;&#50;&#125;&#94;&#123;&#45;&#49;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"48\" style=\"vertical-align: 0px;\" \/> b) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-7e89ac79f87d7fd4e5a6fedc2095eba7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#52;&#92;&#99;&#100;&#111;&#116;&#32;&#50;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#94;&#123;&#45;&#49;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"60\" style=\"vertical-align: -5px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1169597684591\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<table id=\"eip-779\" class=\"unnumbered unstyled\" summary=\"\/\">\n<tbody>\n<tr>\n<td>a)<br \/>\nDo exponents before multiplication.<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-cc2b16c6b1626c739c80ba4aefc5f6fa_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#52;&#92;&#99;&#100;&#111;&#116;&#123;&#50;&#125;&#94;&#123;&#45;&#49;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"48\" style=\"vertical-align: 0px;\" \/><\/td>\n<\/tr>\n<tr>\n<td>Use <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-2e4ab25b3a2e5c55ac5d165362a31987_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#97;&#125;&#94;&#123;&#45;&#110;&#125;&#61;&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#123;&#97;&#125;&#94;&#123;&#110;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"71\" style=\"vertical-align: -6px;\" \/>.<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-2b6e893f98dab02431cc8bb3070335e8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#52;&#92;&#99;&#100;&#111;&#116;&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#123;&#50;&#125;&#94;&#123;&#49;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"23\" width=\"38\" style=\"vertical-align: -7px;\" \/><\/td>\n<\/tr>\n<tr>\n<td>Simplify.<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-8c6633954227aa72b608b60e92fe0c7c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"8\" style=\"vertical-align: 0px;\" \/><\/td>\n<\/tr>\n<tr>\n<td>b)<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-7e89ac79f87d7fd4e5a6fedc2095eba7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#52;&#92;&#99;&#100;&#111;&#116;&#32;&#50;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#94;&#123;&#45;&#49;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"60\" style=\"vertical-align: -5px;\" \/><\/td>\n<\/tr>\n<tr>\n<td>Simplify inside the parentheses first.<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-8d0aa8a95de1753e6b7fbb3ea7988342_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#56;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#94;&#123;&#45;&#49;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"39\" style=\"vertical-align: -5px;\" \/><\/td>\n<\/tr>\n<tr>\n<td>Use <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-2e4ab25b3a2e5c55ac5d165362a31987_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#97;&#125;&#94;&#123;&#45;&#110;&#125;&#61;&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#123;&#97;&#125;&#94;&#123;&#110;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"71\" style=\"vertical-align: -6px;\" \/>.<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-6f64929720f61bcc9b1825295477122e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#123;&#56;&#125;&#94;&#123;&#49;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"23\" width=\"14\" style=\"vertical-align: -7px;\" \/><\/td>\n<\/tr>\n<tr>\n<td>Simplify.<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-c2cfa6670ebdcbfaa8e068cc03a9a346_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#56;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"7\" style=\"vertical-align: -6px;\" \/><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 5.1<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169597479266\" data-type=\"problem\">\n<p id=\"fs-id1169597689696\">Simplify: a) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-633ac7207076178160db1e99da8ab57b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#54;&#92;&#99;&#100;&#111;&#116;&#123;&#51;&#125;&#94;&#123;&#45;&#49;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"48\" style=\"vertical-align: 0px;\" \/> \u00a0\u00a0 b) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-b003906d3a8ba4ddff616264c368c4a2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#54;&#92;&#99;&#100;&#111;&#116;&#51;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#94;&#123;&#45;&#49;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"60\" style=\"vertical-align: -5px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1169597576993\" data-type=\"solution\">\n<details>\n<summary>Show answer<\/summary>\n<p id=\"fs-id1169597576996\">a) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-8c6633954227aa72b608b60e92fe0c7c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"8\" style=\"vertical-align: 0px;\" \/> \u00a0\u00a0 b) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-5dff629988fe694142a630046bce4791_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#49;&#56;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"14\" style=\"vertical-align: -6px;\" \/><\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1169597479261\" class=\"try\" data-type=\"note\">\n<div data-type=\"exercise\">\n<div id=\"fs-id1169597576993\" data-type=\"solution\">\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 5.2<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169597577016\" data-type=\"problem\">\n<p id=\"fs-id1169597577018\">Simplify: a) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-7158f11b762d7fc8734404063b240f29_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#56;&#92;&#99;&#100;&#111;&#116;&#123;&#50;&#125;&#94;&#123;&#45;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"49\" style=\"vertical-align: 0px;\" \/> \u00a0\u00a0 b) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-74c840c8109fbb403589b089990afcf9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#56;&#92;&#99;&#100;&#111;&#116;&#32;&#50;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#94;&#123;&#45;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"61\" style=\"vertical-align: -5px;\" \/>.<\/p>\n<\/div>\n<div data-type=\"solution\">\n<details>\n<summary>Show answer<\/summary>\n<p id=\"fs-id1169597533015\">a) 2 \u00a0\u00a0 b) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-ec216051bb2907f5ebc1bc3ba3ac0208_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#50;&#53;&#54;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"21\" style=\"vertical-align: -6px;\" \/><\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<p id=\"fs-id1169597689365\">When a variable is raised to a negative exponent, we apply the definition the same way we did with numbers. We will assume all variables are non-zero.<\/p>\n<div class=\"textbox textbox--examples\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 6<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169597479240\" data-type=\"problem\">\n<p id=\"fs-id1169597479242\">Simplify: a) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-8dd42e09d3f8a96dc1512e9b7b36ac70_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#120;&#125;&#94;&#123;&#45;&#54;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"28\" style=\"vertical-align: 0px;\" \/> \u00a0\u00a0 b) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-3b0a842880e63250601249af1d29e100_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#123;&#117;&#125;&#94;&#123;&#52;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#94;&#123;&#45;&#51;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"26\" width=\"50\" style=\"vertical-align: -7px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1169597688171\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<div data-type=\"title\">\n<table style=\"border-collapse: collapse;width: 100%\">\n<tbody>\n<tr>\n<td style=\"width: 50%\">a)<\/td>\n<td style=\"width: 50%\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-8dd42e09d3f8a96dc1512e9b7b36ac70_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#120;&#125;&#94;&#123;&#45;&#54;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"28\" style=\"vertical-align: 0px;\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%\">Use the definition of a negative exponent <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-2e4ab25b3a2e5c55ac5d165362a31987_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#97;&#125;&#94;&#123;&#45;&#110;&#125;&#61;&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#123;&#97;&#125;&#94;&#123;&#110;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"71\" style=\"vertical-align: -6px;\" \/><\/td>\n<td style=\"width: 50%\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-dfbe602094fe1136f84556702820356b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#123;&#120;&#125;&#94;&#123;&#54;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"23\" width=\"15\" style=\"vertical-align: -7px;\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%\">b)<\/td>\n<td style=\"width: 50%\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-3b0a842880e63250601249af1d29e100_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#123;&#117;&#125;&#94;&#123;&#52;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#94;&#123;&#45;&#51;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"26\" width=\"50\" style=\"vertical-align: -7px;\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%\">Use the definition of a negative exponent <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-2e4ab25b3a2e5c55ac5d165362a31987_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#97;&#125;&#94;&#123;&#45;&#110;&#125;&#61;&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#123;&#97;&#125;&#94;&#123;&#110;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"71\" style=\"vertical-align: -6px;\" \/>.<\/td>\n<td style=\"width: 50%\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-c0d325ad00c3a23745bfc553e65f1d37_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#123;&#117;&#125;&#94;&#123;&#52;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#94;&#123;&#51;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"29\" width=\"33\" style=\"vertical-align: -13px;\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%\">Simplify.<\/td>\n<td style=\"width: 50%\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-47d2c3afb6402646c1f96dce48e05201_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#123;&#117;&#125;&#94;&#123;&#49;&#50;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"23\" width=\"21\" style=\"vertical-align: -7px;\" \/><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 6.1<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169597478468\" data-type=\"problem\">\n<p id=\"fs-id1169597541016\">Simplify: a) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-1b296cce89bcc5ad8dff21de6c74a578_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#121;&#125;&#94;&#123;&#45;&#55;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"27\" style=\"vertical-align: -4px;\" \/> \u00a0\u00a0 b) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-3573ec480cccc332a1f0e5fd1d847b17_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#123;&#122;&#125;&#94;&#123;&#51;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#94;&#123;&#45;&#53;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"26\" width=\"49\" style=\"vertical-align: -7px;\" \/><\/p>\n<\/div>\n<div id=\"fs-id1169597378928\" data-type=\"solution\">\n<details>\n<summary>Show answer<\/summary>\n<p id=\"fs-id1169597479516\">a) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-59c5ba9b0465281f3d4798c7af6cae0d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#123;&#121;&#125;&#94;&#123;&#55;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"26\" width=\"15\" style=\"vertical-align: -10px;\" \/> \u00a0\u00a0 b) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-d35ca3be2ea8440b39bf894c0f93bd53_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#123;&#122;&#125;&#94;&#123;&#49;&#53;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"23\" width=\"20\" style=\"vertical-align: -7px;\" \/><\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1169597478463\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1169597478466\" data-type=\"exercise\">\n<div id=\"fs-id1169597478468\" data-type=\"problem\">\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 6.2<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169597507834\" data-type=\"problem\">\n<p id=\"fs-id1169597507836\">Simplify: a) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-0c938ce7d303d487e5549541fcc5387d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#112;&#125;&#94;&#123;&#45;&#57;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"28\" style=\"vertical-align: -4px;\" \/> \u00a0\u00a0 b) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-ff2b94c58f333a955a61a8ea4f8f6ec3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#123;&#113;&#125;&#94;&#123;&#52;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#94;&#123;&#45;&#54;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"26\" width=\"48\" style=\"vertical-align: -7px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1169597689772\" data-type=\"solution\">\n<details>\n<summary>Show answer<\/summary>\n<p id=\"fs-id1169597689774\">a) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-3e6d6de079405c52a8517d36397724f3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#123;&#112;&#125;&#94;&#123;&#57;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"26\" width=\"15\" style=\"vertical-align: -10px;\" \/> \u00a0\u00a0 b) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-6e0c3e656c26e2308e4c41888b4c85dc_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#123;&#113;&#125;&#94;&#123;&#50;&#52;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"26\" width=\"20\" style=\"vertical-align: -10px;\" \/><\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<p id=\"fs-id1169597539260\">When there is a product and an exponent we have to be careful to apply the exponent to the correct quantity. According to the Order of Operations, we simplify expressions in parentheses before applying exponents. We\u2019ll see how this works in the next example.<\/p>\n<div class=\"textbox textbox--examples\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 7<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169597688873\" data-type=\"problem\">\n<p id=\"fs-id1169597688875\">Simplify: a) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-33bc086540899ff130b8c07e62527cce_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#53;&#123;&#121;&#125;&#94;&#123;&#45;&#49;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"35\" style=\"vertical-align: -4px;\" \/> \u00a0\u00a0 b) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-f4a45a0a1b70c5134c3655df0c3a2178_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#53;&#121;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#94;&#123;&#45;&#49;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"48\" style=\"vertical-align: -5px;\" \/> c) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-740fad5d4dc0f39cb3332762392cd7fa_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#53;&#121;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#94;&#123;&#45;&#49;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"62\" style=\"vertical-align: -5px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1169597690063\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<div data-type=\"title\">\n<table style=\"border-collapse: collapse;width: 100%;height: 140px\">\n<tbody>\n<tr style=\"height: 14px\">\n<td style=\"width: 50%;height: 14px\">a) Notice the exponent applies to just the base.<\/td>\n<td style=\"width: 50%;height: 14px\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-33bc086540899ff130b8c07e62527cce_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#53;&#123;&#121;&#125;&#94;&#123;&#45;&#49;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"35\" style=\"vertical-align: -4px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 14px\">\n<td style=\"width: 50%;height: 14px\">Take the reciprocal of <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-15f1a95c39a36eda2e95d509a5f0f8b9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"9\" style=\"vertical-align: -4px;\" \/> and change the sign of the exponent.<\/td>\n<td style=\"width: 50%;height: 14px\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-ee400a187d89017d68ac00735b20efc0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#53;&#92;&#99;&#100;&#111;&#116;&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#123;&#121;&#125;&#94;&#123;&#49;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"26\" width=\"39\" style=\"vertical-align: -10px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 14px\">\n<td style=\"width: 50%;height: 14px\">Simplify.<\/td>\n<td style=\"width: 50%;height: 14px\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-35f6264dfc07aeff8deb6f7ee4864bdc_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#53;&#125;&#123;&#121;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"25\" width=\"8\" style=\"vertical-align: -9px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 14px\">\n<td style=\"width: 50%;height: 14px\">b) Here the parentheses make the exponent apply to the base.<\/td>\n<td style=\"width: 50%;height: 14px\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-f4a45a0a1b70c5134c3655df0c3a2178_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#53;&#121;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#94;&#123;&#45;&#49;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"48\" style=\"vertical-align: -5px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 14px\">\n<td style=\"width: 50%;height: 14px\">Take the reciprocal of <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-5634f0fd5254c639e7023f0f6cca0d33_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#53;&#121;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"18\" style=\"vertical-align: -4px;\" \/> and change the sign of the exponent.<\/td>\n<td style=\"width: 50%;height: 14px\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-86fe8563ea2f999add5de213a9c1b24f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#53;&#121;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#94;&#123;&#49;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"29\" width=\"32\" style=\"vertical-align: -13px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 14px\">\n<td style=\"width: 50%;height: 14px\">Simplify.<\/td>\n<td style=\"width: 50%;height: 14px\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-bb7abd6227da7be0ecdf9c9bd072b18f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#53;&#121;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"25\" width=\"15\" style=\"vertical-align: -9px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 14px\">\n<td style=\"width: 50%;height: 14px\">c) The base here is <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-90a5f18918a3859008b4d0667f32a811_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#53;&#121;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"31\" style=\"vertical-align: -4px;\" \/>.<\/td>\n<td style=\"width: 50%;height: 14px\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-740fad5d4dc0f39cb3332762392cd7fa_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#53;&#121;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#94;&#123;&#45;&#49;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"62\" style=\"vertical-align: -5px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 14px\">\n<td style=\"width: 50%;height: 14px\">Take the reciprocal of <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-90a5f18918a3859008b4d0667f32a811_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#53;&#121;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"31\" style=\"vertical-align: -4px;\" \/> and change the sign of the exponent.<\/td>\n<td style=\"width: 50%;height: 14px\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-ef66117f5eb50de15d6c53e2b9edf057_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#53;&#121;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#94;&#123;&#49;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"29\" width=\"43\" style=\"vertical-align: -13px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 14px\">\n<td style=\"width: 50%;height: 14px\">Simplify.<\/td>\n<td style=\"width: 50%;height: 14px\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-4f2e4ce6e47c79e27fe70eb196e0357c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#45;&#53;&#121;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"25\" width=\"25\" style=\"vertical-align: -9px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 14px\">\n<td style=\"width: 50%;height: 14px\">Use <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-428a1bcbde7e957ea7fea772217f6e61_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#97;&#125;&#123;&#45;&#98;&#125;&#61;&#45;&#92;&#102;&#114;&#97;&#99;&#123;&#97;&#125;&#123;&#98;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"66\" style=\"vertical-align: -6px;\" \/><\/td>\n<td style=\"width: 50%;height: 14px\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-1125bb240333512ee8565aca9998af37_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#53;&#121;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"25\" width=\"30\" style=\"vertical-align: -9px;\" \/><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 7.1<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169597691040\" data-type=\"problem\">\n<p id=\"fs-id1169597691042\">Simplify: a) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-43de735228d85c142995632b9e38020a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#56;&#123;&#112;&#125;&#94;&#123;&#45;&#49;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"35\" style=\"vertical-align: -4px;\" \/> b) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-fa1ab335dcd8611cb0d5d655548920a9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#56;&#112;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#94;&#123;&#45;&#49;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"48\" style=\"vertical-align: -5px;\" \/> c) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-85e9f63039898ba350caa9fd90004fc6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#56;&#112;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#94;&#123;&#45;&#49;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"61\" style=\"vertical-align: -5px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1169597539540\" data-type=\"solution\">\n<details>\n<summary>Show answer<\/summary>\n<p id=\"fs-id1169597539542\">a) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-21bb8e2d7c9ebb616d55f4b0f6741313_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#56;&#125;&#123;&#112;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"25\" width=\"8\" style=\"vertical-align: -9px;\" \/> b) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-838418bc3e6f6ebd989ac5399c1c35e0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#56;&#112;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"25\" width=\"14\" style=\"vertical-align: -9px;\" \/> c) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-e82b898f023730283cdcfc5af1a683e4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#56;&#112;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"25\" width=\"29\" style=\"vertical-align: -9px;\" \/><\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1169597691035\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1169597691038\" data-type=\"exercise\">\n<div id=\"fs-id1169597691040\" data-type=\"problem\">\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 7.2<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div data-type=\"problem\">\n<p>Simplify: a) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-286528f71c8122c79c268eb235679df3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#49;&#49;&#113;&#125;&#94;&#123;&#45;&#49;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"42\" style=\"vertical-align: -4px;\" \/>\u00a0 \u00a0b) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-bdfd217f2ef3e69c778c697da8594061_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#49;&#49;&#113;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#94;&#123;&#45;&#49;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"56\" style=\"vertical-align: -5px;\" \/>\u00a0 c) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-fc664b20c178ed5a1cdf4eb1ab6e9ce4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#49;&#49;&#113;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#94;&#123;&#45;&#49;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"70\" style=\"vertical-align: -5px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1169597738793\" data-type=\"solution\">\n<details>\n<summary>Show answer<\/summary>\n<p id=\"fs-id1169597738795\">a) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-803b2d81c951555fb83fc3de87549f2f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#49;&#125;&#123;&#113;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"25\" width=\"14\" style=\"vertical-align: -9px;\" \/>\u00a0 \u00a0b) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-57235d991e9da01ada5ce673dbf6f020_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#49;&#49;&#113;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"25\" width=\"21\" style=\"vertical-align: -9px;\" \/>\u00a0 \u00a0c) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-cbbae5330cbe784a67f62d0d4991e1e8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#49;&#49;&#113;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"25\" width=\"36\" style=\"vertical-align: -9px;\" \/><\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<p>With negative exponents, the Quotient Rule needs only one form <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-b53c161692a009bf4009109559541202_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#123;&#97;&#125;&#94;&#123;&#109;&#125;&#125;&#123;&#123;&#97;&#125;&#94;&#123;&#110;&#125;&#125;&#61;&#123;&#97;&#125;&#94;&#123;&#109;&#45;&#110;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"23\" width=\"84\" style=\"vertical-align: -6px;\" \/>, for <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-dfe13c0744369e0c0709de8599d9455f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#97;&#92;&#110;&#101;&#32;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"42\" style=\"vertical-align: -4px;\" \/>. When the exponent in the denominator is larger than the exponent in the numerator, the exponent of the quotient will be negative.<\/p>\n<\/div>\n<\/div>\n<\/div>\n<h1>Simplify Expressions with Integer Exponents<\/h1>\n<p id=\"fs-id1169597539593\">All of the exponent properties we developed earlier in the chapter with whole number exponents apply to integer exponents, too. We restate them here for reference.<\/p>\n<div id=\"fs-id1169597539598\" data-type=\"note\">\n<div data-type=\"title\">\n<div class=\"textbox textbox--key-takeaways\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">Summary of Exponent Properties<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<p id=\"fs-id1169597688590\">If <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-9bd295ba1eac106832650cda85daba43_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#97;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#97;&#110;&#100;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#98;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"53\" style=\"vertical-align: -1px;\" \/> are real numbers, and <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-8fe1b94dcc47778394ca62ab7c8655e0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#109;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#97;&#110;&#100;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#110;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"62\" style=\"vertical-align: -1px;\" \/> are integers, then<\/p>\n<div class=\"unnumbered\" data-type=\"equation\" data-label=\"\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-ad276f7c1e93ced92af2d382a3d53f98_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#98;&#101;&#103;&#105;&#110;&#123;&#97;&#114;&#114;&#97;&#121;&#125;&#123;&#99;&#99;&#99;&#99;&#99;&#99;&#125;&#92;&#109;&#97;&#116;&#104;&#98;&#102;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#80;&#114;&#111;&#100;&#117;&#99;&#116;&#32;&#80;&#114;&#111;&#112;&#101;&#114;&#116;&#121;&#125;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#38;&#32;&#38;&#32;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#123;&#97;&#125;&#94;&#123;&#109;&#125;&#92;&#99;&#100;&#111;&#116;&#123;&#97;&#125;&#94;&#123;&#110;&#125;&#38;&#32;&#61;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#123;&#97;&#125;&#94;&#123;&#109;&#43;&#110;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#92;&#32;&#92;&#109;&#97;&#116;&#104;&#98;&#102;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#80;&#111;&#119;&#101;&#114;&#32;&#80;&#114;&#111;&#112;&#101;&#114;&#116;&#121;&#125;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#38;&#32;&#38;&#32;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#123;&#97;&#125;&#94;&#123;&#109;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#94;&#123;&#110;&#125;&#38;&#32;&#61;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#123;&#97;&#125;&#94;&#123;&#109;&#92;&#99;&#100;&#111;&#116;&#32;&#110;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#92;&#32;&#92;&#109;&#97;&#116;&#104;&#98;&#102;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#80;&#114;&#111;&#100;&#117;&#99;&#116;&#32;&#116;&#111;&#32;&#97;&#32;&#80;&#111;&#119;&#101;&#114;&#125;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#38;&#32;&#38;&#32;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#97;&#98;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#94;&#123;&#109;&#125;&#38;&#32;&#61;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#123;&#97;&#125;&#94;&#123;&#109;&#125;&#123;&#98;&#125;&#94;&#123;&#109;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#92;&#32;&#92;&#109;&#97;&#116;&#104;&#98;&#102;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#81;&#117;&#111;&#116;&#105;&#101;&#110;&#116;&#32;&#80;&#114;&#111;&#112;&#101;&#114;&#116;&#121;&#125;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#38;&#32;&#38;&#32;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#102;&#114;&#97;&#99;&#123;&#123;&#97;&#125;&#94;&#123;&#109;&#125;&#125;&#123;&#123;&#97;&#125;&#94;&#123;&#110;&#125;&#125;&#38;&#32;&#61;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#123;&#97;&#125;&#94;&#123;&#109;&#45;&#110;&#125;&#44;&#97;&#92;&#110;&#101;&#32;&#48;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#92;&#32;&#92;&#109;&#97;&#116;&#104;&#98;&#102;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#90;&#101;&#114;&#111;&#32;&#69;&#120;&#112;&#111;&#110;&#101;&#110;&#116;&#32;&#80;&#114;&#111;&#112;&#101;&#114;&#116;&#121;&#125;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#38;&#32;&#38;&#32;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#123;&#97;&#125;&#94;&#123;&#48;&#125;&#38;&#32;&#61;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#49;&#44;&#97;&#92;&#110;&#101;&#32;&#48;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#92;&#32;&#92;&#109;&#97;&#116;&#104;&#98;&#102;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#81;&#117;&#111;&#116;&#105;&#101;&#110;&#116;&#32;&#116;&#111;&#32;&#97;&#32;&#80;&#111;&#119;&#101;&#114;&#32;&#80;&#114;&#111;&#112;&#101;&#114;&#116;&#121;&#125;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#38;&#32;&#38;&#32;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#92;&#102;&#114;&#97;&#99;&#123;&#97;&#125;&#123;&#98;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#94;&#123;&#109;&#125;&#38;&#32;&#61;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#92;&#102;&#114;&#97;&#99;&#123;&#123;&#97;&#125;&#94;&#123;&#109;&#125;&#125;&#123;&#123;&#98;&#125;&#94;&#123;&#109;&#125;&#125;&#44;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#98;&#92;&#110;&#101;&#32;&#48;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#92;&#32;&#92;&#109;&#97;&#116;&#104;&#98;&#102;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#80;&#114;&#111;&#112;&#101;&#114;&#116;&#105;&#101;&#115;&#32;&#111;&#102;&#32;&#78;&#101;&#103;&#97;&#116;&#105;&#118;&#101;&#32;&#69;&#120;&#112;&#111;&#110;&#101;&#110;&#116;&#115;&#125;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#38;&#32;&#38;&#32;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#123;&#97;&#125;&#94;&#123;&#45;&#110;&#125;&#38;&#32;&#61;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#123;&#97;&#125;&#94;&#123;&#110;&#125;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#53;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#97;&#110;&#100;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#53;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#123;&#97;&#125;&#94;&#123;&#45;&#110;&#125;&#125;&#61;&#123;&#97;&#125;&#94;&#123;&#110;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#92;&#32;&#92;&#109;&#97;&#116;&#104;&#98;&#102;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#81;&#117;&#111;&#116;&#105;&#101;&#110;&#116;&#32;&#116;&#111;&#32;&#97;&#32;&#78;&#101;&#103;&#97;&#116;&#105;&#118;&#101;&#32;&#69;&#120;&#112;&#111;&#110;&#101;&#110;&#116;&#125;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#38;&#32;&#38;&#32;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#92;&#102;&#114;&#97;&#99;&#123;&#97;&#125;&#123;&#98;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#94;&#123;&#45;&#110;&#125;&#38;&#32;&#61;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#92;&#102;&#114;&#97;&#99;&#123;&#98;&#125;&#123;&#97;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#94;&#123;&#110;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#101;&#110;&#100;&#123;&#97;&#114;&#114;&#97;&#121;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"178\" width=\"545\" style=\"vertical-align: -85px;\" \/><\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"unnumbered\" data-type=\"equation\" data-label=\"\">\n<div class=\"textbox textbox--examples\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 8<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169597741131\" data-type=\"problem\">\n<p id=\"fs-id1169597741133\">Simplify: a) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-4a7d55ebb1ffd30a99fd6a42931006dd_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#120;&#125;&#94;&#123;&#45;&#52;&#125;&#92;&#99;&#100;&#111;&#116;&#123;&#120;&#125;&#94;&#123;&#54;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"58\" style=\"vertical-align: 0px;\" \/> b) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-b2dd63d4caa28193bd52eb4e3df9490c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#121;&#125;&#94;&#123;&#45;&#54;&#125;&#92;&#99;&#100;&#111;&#116;&#123;&#121;&#125;&#94;&#123;&#52;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"57\" style=\"vertical-align: -4px;\" \/> c) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-06a597987d41eb2fb44be2d1e7e90520_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#122;&#125;&#94;&#123;&#45;&#53;&#125;&#92;&#99;&#100;&#111;&#116;&#123;&#122;&#125;&#94;&#123;&#45;&#51;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"67\" style=\"vertical-align: 0px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1169597508211\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<div data-type=\"title\"><\/div>\n<ol id=\"fs-id1168746443625\" class=\"circled\" type=\"a\">\n<li>\n<table style=\"border-collapse: collapse;width: 100%;height: 42px\">\n<tbody>\n<tr style=\"height: 14px\">\n<td style=\"width: 50%;height: 14px\"><\/td>\n<td style=\"width: 50%;height: 14px\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-4a7d55ebb1ffd30a99fd6a42931006dd_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#120;&#125;&#94;&#123;&#45;&#52;&#125;&#92;&#99;&#100;&#111;&#116;&#123;&#120;&#125;&#94;&#123;&#54;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"58\" style=\"vertical-align: 0px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 14px\">\n<td style=\"width: 50%;height: 14px\">Use the Product Property, <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-e3c8d65b201733621a9fe814232eb82c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#97;&#125;&#94;&#123;&#109;&#125;&#92;&#99;&#100;&#111;&#116;&#123;&#97;&#125;&#94;&#123;&#110;&#125;&#61;&#123;&#97;&#125;&#94;&#123;&#109;&#43;&#110;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"117\" style=\"vertical-align: 0px;\" \/>.<\/td>\n<td style=\"width: 50%;height: 14px\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-8caa4359bb8bd44315c87d9f16d1373c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#120;&#125;&#94;&#123;&#45;&#52;&#43;&#54;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"46\" style=\"vertical-align: 0px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 14px\">\n<td style=\"width: 50%;height: 14px\">Simplify<\/td>\n<td style=\"width: 50%;height: 14px\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-60a826196aae662bd64e5dd6bbd1fafd_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#120;&#125;&#94;&#123;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"17\" style=\"vertical-align: 0px;\" \/><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/li>\n<li>\n<table style=\"border-collapse: collapse;width: 100%\">\n<tbody>\n<tr>\n<td style=\"width: 50%\"><\/td>\n<td style=\"width: 50%\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-b2dd63d4caa28193bd52eb4e3df9490c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#121;&#125;&#94;&#123;&#45;&#54;&#125;&#92;&#99;&#100;&#111;&#116;&#123;&#121;&#125;&#94;&#123;&#52;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"57\" style=\"vertical-align: -4px;\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%\">Notice the same bases, so add the exponents.<\/td>\n<td style=\"width: 50%\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-e5c013f8445aaa3aece65cda4d79129b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#121;&#125;&#94;&#123;&#45;&#54;&#43;&#52;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"45\" style=\"vertical-align: -4px;\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%\">Simplify.<\/td>\n<td style=\"width: 50%\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-fd7305dbe51cddd0e0e4b2204a08162a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#121;&#125;&#94;&#123;&#45;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"27\" style=\"vertical-align: -4px;\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%\">Use the definition of a negative exponent, <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-8e186e09dd0c76cc9e4528e25a944aeb_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#123;&#97;&#125;&#94;&#123;&#110;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"16\" style=\"vertical-align: -6px;\" \/>.<\/td>\n<td style=\"width: 50%\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-d0b80691efcb015d76a52f8b64cc2cfe_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#123;&#121;&#125;&#94;&#123;&#50;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"26\" width=\"15\" style=\"vertical-align: -10px;\" \/><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/li>\n<li>\n<table style=\"border-collapse: collapse;width: 100%\">\n<tbody>\n<tr>\n<td style=\"width: 50%\"><\/td>\n<td style=\"width: 50%\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-06a597987d41eb2fb44be2d1e7e90520_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#122;&#125;&#94;&#123;&#45;&#53;&#125;&#92;&#99;&#100;&#111;&#116;&#123;&#122;&#125;&#94;&#123;&#45;&#51;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"67\" style=\"vertical-align: 0px;\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%\">Add the exponents, since the bases are the same.<\/td>\n<td style=\"width: 50%\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-092ef29b8fad3b1aa1cf970807febde3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#122;&#125;&#94;&#123;&#45;&#53;&#45;&#51;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"45\" style=\"vertical-align: 0px;\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%\">Simplify.<\/td>\n<td style=\"width: 50%\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-597ccc0b46a9319a5d5d70122e18085a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#122;&#125;&#94;&#123;&#45;&#56;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"27\" style=\"vertical-align: 0px;\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%\">Take the reciprocal and change the sign of the exponent, using the definition of a negative exponent.<\/td>\n<td style=\"width: 50%\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-ca32aae137675a3f96edb2035a0973e8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#123;&#122;&#125;&#94;&#123;&#56;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"23\" width=\"14\" style=\"vertical-align: -7px;\" \/><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/li>\n<\/ol>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 8.1<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169597395207\" data-type=\"problem\">\n<p id=\"fs-id1169597395209\">Simplify: a) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-36c3fd169c254d794fc79e1e9d8a57f9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#120;&#125;&#94;&#123;&#45;&#51;&#125;&#92;&#99;&#100;&#111;&#116;&#123;&#120;&#125;&#94;&#123;&#55;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"58\" style=\"vertical-align: 0px;\" \/> b) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-704c0da8cc01fd964326d74195a437e8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#121;&#125;&#94;&#123;&#45;&#55;&#125;&#92;&#99;&#100;&#111;&#116;&#123;&#121;&#125;&#94;&#123;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"57\" style=\"vertical-align: -4px;\" \/> c) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-c6135328fb9d447e3509f37bec6c4e32_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#122;&#125;&#94;&#123;&#45;&#52;&#125;&#92;&#99;&#100;&#111;&#116;&#123;&#122;&#125;&#94;&#123;&#45;&#53;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"67\" style=\"vertical-align: 0px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1169597537212\" data-type=\"solution\">\n<details>\n<summary>Show answer<\/summary>\n<p id=\"fs-id1169597537214\">a) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-021ca79c791ef12b1eece3bb900d6dfc_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#120;&#125;&#94;&#123;&#52;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"17\" style=\"vertical-align: 0px;\" \/> b) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-a6d8c1210fd32bb0ee041a602283db67_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#123;&#121;&#125;&#94;&#123;&#53;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"26\" width=\"15\" style=\"vertical-align: -10px;\" \/> c) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-fe84f5490650e59e10279d517ece42db_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#123;&#122;&#125;&#94;&#123;&#57;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"23\" width=\"14\" style=\"vertical-align: -7px;\" \/><\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 8.2<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169597688417\" data-type=\"problem\">\n<p id=\"fs-id1169597688420\">Simplify: a) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-21ceadda2dfde6f303338d7802478a7c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#97;&#125;&#94;&#123;&#45;&#49;&#125;&#92;&#99;&#100;&#111;&#116;&#123;&#97;&#125;&#94;&#123;&#54;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"57\" style=\"vertical-align: 0px;\" \/> b) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-03d4f52a2f7b776b41fbc178fbe94ed4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#98;&#125;&#94;&#123;&#45;&#56;&#125;&#92;&#99;&#100;&#111;&#116;&#123;&#98;&#125;&#94;&#123;&#52;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"54\" style=\"vertical-align: 0px;\" \/> c) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-baf4ecd05bbf37ec06e941d095c0feba_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#99;&#125;&#94;&#123;&#45;&#56;&#125;&#92;&#99;&#100;&#111;&#116;&#123;&#99;&#125;&#94;&#123;&#45;&#55;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"65\" style=\"vertical-align: 0px;\" \/>.<\/p>\n<\/div>\n<div data-type=\"solution\">\n<details>\n<summary>Show answer<\/summary>\n<p>a) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-32f8e0ba4a319c25b5a56cf0b1bcaf63_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#97;&#125;&#94;&#123;&#53;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"16\" style=\"vertical-align: 0px;\" \/> b) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-fac7b6712ef01071713e2b2bc541e214_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#123;&#98;&#125;&#94;&#123;&#52;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"23\" width=\"13\" style=\"vertical-align: -7px;\" \/> c) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-0b02fc4dbb947a4fd1c206470a607b6a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#123;&#99;&#125;&#94;&#123;&#49;&#53;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"23\" width=\"19\" style=\"vertical-align: -7px;\" \/><\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<p id=\"fs-id1169597507987\">In the next two examples, we\u2019ll start by using the Commutative Property to group the same variables together. This makes it easier to identify the like bases before using the Product Property.<\/p>\n<div class=\"textbox textbox--examples\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 9<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169597687992\" data-type=\"problem\">\n<p id=\"fs-id1169597687994\">Simplify: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-e7e4c87a680fed382682579b53afb690_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#123;&#109;&#125;&#94;&#123;&#52;&#125;&#123;&#110;&#125;&#94;&#123;&#45;&#51;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#108;&#101;&#102;&#116;&#40;&#123;&#109;&#125;&#94;&#123;&#45;&#53;&#125;&#123;&#110;&#125;&#94;&#123;&#45;&#50;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"147\" style=\"vertical-align: -7px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1169597479130\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<div data-type=\"title\">\n<table style=\"border-collapse: collapse;width: 100%\">\n<tbody>\n<tr>\n<td style=\"width: 50%\"><\/td>\n<td style=\"width: 50%\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-e7e4c87a680fed382682579b53afb690_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#123;&#109;&#125;&#94;&#123;&#52;&#125;&#123;&#110;&#125;&#94;&#123;&#45;&#51;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#108;&#101;&#102;&#116;&#40;&#123;&#109;&#125;&#94;&#123;&#45;&#53;&#125;&#123;&#110;&#125;&#94;&#123;&#45;&#50;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"147\" style=\"vertical-align: -7px;\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%\">Use the Commutative Property to get like bases together.<\/td>\n<td style=\"width: 50%\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-c24db09768a7d8f0758c431c5b053b7a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#109;&#125;&#94;&#123;&#52;&#125;&#123;&#109;&#125;&#94;&#123;&#45;&#53;&#125;&#92;&#99;&#100;&#111;&#116;&#123;&#110;&#125;&#94;&#123;&#45;&#50;&#125;&#123;&#110;&#125;&#94;&#123;&#45;&#51;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"128\" style=\"vertical-align: 0px;\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%\">Add the exponents for each base.<\/td>\n<td style=\"width: 50%\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-534849ce8f7d3ff60905a3dfd9631756_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#109;&#125;&#94;&#123;&#45;&#49;&#125;&#92;&#99;&#100;&#111;&#116;&#123;&#110;&#125;&#94;&#123;&#45;&#53;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"76\" style=\"vertical-align: 0px;\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%\">Take the reciprocals and change the signs of the exponents.<\/td>\n<td style=\"width: 50%\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-5864761fa9fb3ceed1e249f797ca1f81_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#123;&#109;&#125;&#94;&#123;&#49;&#125;&#125;&#92;&#99;&#100;&#111;&#116;&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#123;&#110;&#125;&#94;&#123;&#53;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"23\" width=\"52\" style=\"vertical-align: -7px;\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%\">Simplify.<\/td>\n<td style=\"width: 50%\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-41267d84ad4c940890875e9b8aa604f6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#109;&#123;&#110;&#125;&#94;&#123;&#53;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"23\" width=\"28\" style=\"vertical-align: -7px;\" \/><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 9.1<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div data-type=\"problem\">\n<p>Simplify: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-8488ac2413cc0c53caf25a989760c387_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#123;&#112;&#125;&#94;&#123;&#54;&#125;&#123;&#113;&#125;&#94;&#123;&#45;&#50;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#108;&#101;&#102;&#116;&#40;&#123;&#112;&#125;&#94;&#123;&#45;&#57;&#125;&#123;&#113;&#125;&#94;&#123;&#45;&#49;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"129\" style=\"vertical-align: -7px;\" \/>.<\/p>\n<\/div>\n<div data-type=\"solution\">\n<details>\n<summary>Show answer<\/summary>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-6d2523d86eccd4dc5e341c45b53f07bf_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#123;&#112;&#125;&#94;&#123;&#51;&#125;&#123;&#113;&#125;&#94;&#123;&#51;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"26\" width=\"29\" style=\"vertical-align: -10px;\" \/><\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1169597689068\" class=\"try\" data-type=\"note\">\n<div data-type=\"exercise\">\n<div data-type=\"solution\">\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 9.2<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169597461048\" data-type=\"problem\">\n<p id=\"fs-id1169597461050\">Simplify: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-179c89b74291edac16cb3eb37806ffbb_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#123;&#114;&#125;&#94;&#123;&#53;&#125;&#123;&#115;&#125;&#94;&#123;&#45;&#51;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#108;&#101;&#102;&#116;&#40;&#123;&#114;&#125;&#94;&#123;&#45;&#55;&#125;&#123;&#115;&#125;&#94;&#123;&#45;&#53;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"128\" style=\"vertical-align: -7px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1169597700111\" data-type=\"solution\">\n<details>\n<summary>Show answer<\/summary>\n<p id=\"fs-id1169597700113\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-57d4c0d0c9315572140cd3d054b7082d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#123;&#114;&#125;&#94;&#123;&#50;&#125;&#123;&#115;&#125;&#94;&#123;&#56;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"23\" width=\"27\" style=\"vertical-align: -7px;\" \/><\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<p id=\"fs-id1169597479193\">If the monomials have numerical coefficients, we multiply the coefficients, just like we did earlier.<\/p>\n<div class=\"textbox textbox--examples\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 10<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169597479200\" data-type=\"problem\">\n<p id=\"fs-id1169597479202\">Simplify: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-ef4fb6f5f9423182a1174e14f953aede_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#50;&#123;&#120;&#125;&#94;&#123;&#45;&#54;&#125;&#123;&#121;&#125;&#94;&#123;&#56;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#53;&#123;&#120;&#125;&#94;&#123;&#53;&#125;&#123;&#121;&#125;&#94;&#123;&#45;&#51;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"154\" style=\"vertical-align: -7px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1169597479466\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<div data-type=\"title\">\n<table style=\"border-collapse: collapse;width: 100%\">\n<tbody>\n<tr>\n<td style=\"width: 50%\"><\/td>\n<td style=\"width: 50%\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-ef4fb6f5f9423182a1174e14f953aede_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#50;&#123;&#120;&#125;&#94;&#123;&#45;&#54;&#125;&#123;&#121;&#125;&#94;&#123;&#56;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#53;&#123;&#120;&#125;&#94;&#123;&#53;&#125;&#123;&#121;&#125;&#94;&#123;&#45;&#51;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"154\" style=\"vertical-align: -7px;\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%\">Rewrite with the like bases together.<\/td>\n<td style=\"width: 50%\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-50d2a7642e8cf83f8e16c8b575d295f3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#53;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#99;&#100;&#111;&#116;&#92;&#108;&#101;&#102;&#116;&#40;&#123;&#120;&#125;&#94;&#123;&#45;&#54;&#125;&#123;&#120;&#125;&#94;&#123;&#53;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#99;&#100;&#111;&#116;&#92;&#108;&#101;&#102;&#116;&#40;&#123;&#121;&#125;&#94;&#123;&#56;&#125;&#123;&#121;&#125;&#94;&#123;&#45;&#51;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"195\" style=\"vertical-align: -7px;\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%\">Multiply the coefficients and add the exponents of each variable.<\/td>\n<td style=\"width: 50%\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-751558803289b1cbe8aaf98d0de48ff6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#49;&#48;&#92;&#99;&#100;&#111;&#116;&#123;&#120;&#125;&#94;&#123;&#45;&#49;&#125;&#92;&#99;&#100;&#111;&#116;&#123;&#121;&#125;&#94;&#123;&#53;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"101\" style=\"vertical-align: -4px;\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%\">Use the definition of a negative exponent, <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-2e4ab25b3a2e5c55ac5d165362a31987_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#97;&#125;&#94;&#123;&#45;&#110;&#125;&#61;&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#123;&#97;&#125;&#94;&#123;&#110;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"71\" style=\"vertical-align: -6px;\" \/>.<\/td>\n<td style=\"width: 50%\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-77a2d59a822e0201b369c9a5a0e31e06_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#49;&#48;&#92;&#99;&#100;&#111;&#116;&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#123;&#120;&#125;&#94;&#123;&#49;&#125;&#125;&#92;&#99;&#100;&#111;&#116;&#123;&#121;&#125;&#94;&#123;&#53;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"23\" width=\"91\" style=\"vertical-align: -7px;\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%\">Simplify.<\/td>\n<td style=\"width: 50%\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-987b2a4221cf42236172311b044768d2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#45;&#49;&#48;&#123;&#121;&#125;&#94;&#123;&#53;&#125;&#125;&#123;&#120;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"26\" width=\"39\" style=\"vertical-align: -6px;\" \/><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 10.1<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169597705546\" data-type=\"problem\">\n<p id=\"fs-id1169597705548\">Simplify: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-e754254c7195849d924a4412c89f8f06_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#51;&#123;&#117;&#125;&#94;&#123;&#45;&#53;&#125;&#123;&#118;&#125;&#94;&#123;&#55;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#52;&#123;&#117;&#125;&#94;&#123;&#52;&#125;&#123;&#118;&#125;&#94;&#123;&#45;&#50;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"154\" style=\"vertical-align: -7px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1169597537162\" data-type=\"solution\">\n<details>\n<summary>Show answer<\/summary>\n<p id=\"fs-id1169597537164\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-2ef063b0414b712d8b94d50644fcfea3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#50;&#123;&#118;&#125;&#94;&#123;&#53;&#125;&#125;&#123;&#117;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"25\" width=\"43\" style=\"vertical-align: -6px;\" \/><\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 10.2<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169597742137\" data-type=\"problem\">\n<p id=\"fs-id1169597742139\">Simplify: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-1c6bec954e485c30b50116bc78e7582f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#54;&#123;&#99;&#125;&#94;&#123;&#45;&#54;&#125;&#123;&#100;&#125;&#94;&#123;&#52;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#53;&#123;&#99;&#125;&#94;&#123;&#45;&#50;&#125;&#123;&#100;&#125;&#94;&#123;&#45;&#49;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"173\" style=\"vertical-align: -7px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1169597743028\" data-type=\"solution\">\n<details>\n<summary>Show answer<\/summary>\n<p id=\"fs-id1169597743031\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-d77bb56e8d17f8077eff4cc4cf49427c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#51;&#48;&#123;&#100;&#125;&#94;&#123;&#51;&#125;&#125;&#123;&#123;&#99;&#125;&#94;&#123;&#56;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"26\" width=\"28\" style=\"vertical-align: -7px;\" \/><\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<p id=\"fs-id1169597688547\">In the next two examples, we\u2019ll use the Power Property and the Product to a Power Property.<\/p>\n<div class=\"textbox textbox--examples\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 11<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169597688557\" data-type=\"problem\">\n<p id=\"fs-id1169597688559\">Simplify: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-05f1ecbc6a34245c3b85103ebf42f647_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#54;&#123;&#107;&#125;&#94;&#123;&#51;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#94;&#123;&#45;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"26\" width=\"59\" style=\"vertical-align: -7px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1169597540810\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<div data-type=\"title\">\n<table style=\"border-collapse: collapse;width: 100%\">\n<tbody>\n<tr>\n<td style=\"width: 50%\"><\/td>\n<td style=\"width: 50%\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-05f1ecbc6a34245c3b85103ebf42f647_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#54;&#123;&#107;&#125;&#94;&#123;&#51;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#94;&#123;&#45;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"26\" width=\"59\" style=\"vertical-align: -7px;\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%\">Use the product to a Power Property, <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-3988474db9b2232a2364541a7c925f28_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#97;&#98;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#94;&#123;&#109;&#125;&#61;&#123;&#97;&#125;&#94;&#123;&#109;&#125;&#123;&#98;&#125;&#94;&#123;&#109;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"109\" style=\"vertical-align: -5px;\" \/>.<\/td>\n<td style=\"width: 50%\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-4a3c7d65e60e9a9d4a5bcbbe094a33a5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#54;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#94;&#123;&#45;&#50;&#125;&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#123;&#107;&#125;&#94;&#123;&#51;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#94;&#123;&#45;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"26\" width=\"92\" style=\"vertical-align: -7px;\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%\">Use the Power Property, <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-51118695a2e3de3cbaa46c847fc603d0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#123;&#97;&#125;&#94;&#123;&#109;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#94;&#123;&#110;&#125;&#61;&#123;&#97;&#125;&#94;&#123;&#109;&#92;&#99;&#100;&#111;&#116;&#32;&#110;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"101\" style=\"vertical-align: -5px;\" \/>.<\/td>\n<td style=\"width: 50%\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-9514d988a6b6535e9e1d0a039a60ffe7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#54;&#125;&#94;&#123;&#45;&#50;&#125;&#123;&#107;&#125;&#94;&#123;&#45;&#54;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"55\" style=\"vertical-align: 0px;\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%\">Use the Definition of a Negative Exponent, <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-2e4ab25b3a2e5c55ac5d165362a31987_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#97;&#125;&#94;&#123;&#45;&#110;&#125;&#61;&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#123;&#97;&#125;&#94;&#123;&#110;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"71\" style=\"vertical-align: -6px;\" \/>.<\/td>\n<td style=\"width: 50%\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-1909cdbbd0ba447f6f8323392a4c7735_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#123;&#54;&#125;&#94;&#123;&#50;&#125;&#125;&#92;&#99;&#100;&#111;&#116;&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#123;&#107;&#125;&#94;&#123;&#54;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"23\" width=\"45\" style=\"vertical-align: -7px;\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%\">Simplify.<\/td>\n<td style=\"width: 50%\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-616395c955326d1039f042fc0dc4f959_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#51;&#54;&#123;&#107;&#125;&#94;&#123;&#54;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"23\" width=\"29\" style=\"vertical-align: -7px;\" \/><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 11.1<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div data-type=\"problem\">\n<p id=\"fs-id1169597537101\">Simplify: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-d50db71dfce122c5771640cb1e285416_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#52;&#123;&#120;&#125;&#94;&#123;&#52;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#94;&#123;&#45;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"26\" width=\"73\" style=\"vertical-align: -7px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1169597537127\" data-type=\"solution\">\n<details>\n<summary>Show answer<\/summary>\n<p id=\"fs-id1169597537129\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-88cb2d5faefeb43b88dbddd05b3e67fa_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#49;&#54;&#123;&#120;&#125;&#94;&#123;&#56;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"23\" width=\"29\" style=\"vertical-align: -7px;\" \/><\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 11.2<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169597478540\" data-type=\"problem\">\n<p id=\"fs-id1169597478542\">Simplify: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-604dcfb306960beb3c182ac7cc2efbd4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#50;&#123;&#98;&#125;&#94;&#123;&#51;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#94;&#123;&#45;&#52;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"26\" width=\"56\" style=\"vertical-align: -7px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1169597688446\" data-type=\"solution\">\n<details>\n<summary>Show answer<\/summary>\n<p id=\"fs-id1169597688449\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-a1b3318e9184fe30537f6a47923a0430_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#49;&#54;&#123;&#98;&#125;&#94;&#123;&#49;&#50;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"23\" width=\"33\" style=\"vertical-align: -7px;\" \/><\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1169597537093\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1169597537097\" data-type=\"exercise\">\n<div data-type=\"problem\">\n<div class=\"textbox textbox--examples\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 12<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169597688473\" data-type=\"problem\">\n<p id=\"fs-id1169597688475\">Simplify: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-81628a0132e52ca41c9ac73c21e8e162_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#53;&#123;&#120;&#125;&#94;&#123;&#45;&#51;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#94;&#123;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"26\" width=\"59\" style=\"vertical-align: -7px;\" \/>.<\/p>\n<\/div>\n<div data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<div data-type=\"title\">\n<table style=\"border-collapse: collapse;width: 100%\">\n<tbody>\n<tr>\n<td style=\"width: 50%\"><\/td>\n<td style=\"width: 50%\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-81628a0132e52ca41c9ac73c21e8e162_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#53;&#123;&#120;&#125;&#94;&#123;&#45;&#51;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#94;&#123;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"26\" width=\"59\" style=\"vertical-align: -7px;\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%\">Use the Product to a Power Property, <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-3988474db9b2232a2364541a7c925f28_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#97;&#98;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#94;&#123;&#109;&#125;&#61;&#123;&#97;&#125;&#94;&#123;&#109;&#125;&#123;&#98;&#125;&#94;&#123;&#109;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"109\" style=\"vertical-align: -5px;\" \/>.<\/td>\n<td style=\"width: 50%\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-efdb4820599046095f3d496f9ceb8440_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#53;&#125;&#94;&#123;&#50;&#125;&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#123;&#120;&#125;&#94;&#123;&#45;&#51;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#94;&#123;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"26\" width=\"68\" style=\"vertical-align: -7px;\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%\">Simplify and multiply the exponents of <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-bb53ce30a3ff5b6ca87fc6e1eb6588a0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"10\" style=\"vertical-align: 0px;\" \/> using the Power Property, <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-51118695a2e3de3cbaa46c847fc603d0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#123;&#97;&#125;&#94;&#123;&#109;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#94;&#123;&#110;&#125;&#61;&#123;&#97;&#125;&#94;&#123;&#109;&#92;&#99;&#100;&#111;&#116;&#32;&#110;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"101\" style=\"vertical-align: -5px;\" \/>.<\/td>\n<td style=\"width: 50%\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-34280b4dd8d5622d7f0f902ddffff8d0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;&#53;&#92;&#99;&#100;&#111;&#116;&#123;&#120;&#125;&#94;&#123;&#45;&#54;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"59\" style=\"vertical-align: 0px;\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%\">Rewrite by using the Definition of a Negative Exponent, <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-2e4ab25b3a2e5c55ac5d165362a31987_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#97;&#125;&#94;&#123;&#45;&#110;&#125;&#61;&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#123;&#97;&#125;&#94;&#123;&#110;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"71\" style=\"vertical-align: -6px;\" \/>.<\/td>\n<td style=\"width: 50%\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-6ff68420e04c7bc19831c75dbdcc6f0b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;&#53;&#92;&#99;&#100;&#111;&#116;&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#123;&#120;&#125;&#94;&#123;&#54;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"23\" width=\"47\" style=\"vertical-align: -7px;\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%\">Simplify.<\/td>\n<td style=\"width: 50%\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-9abe466de559aba2c7d233c5353bb985_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#50;&#53;&#125;&#123;&#123;&#120;&#125;&#94;&#123;&#54;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"23\" width=\"15\" style=\"vertical-align: -7px;\" \/><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1169597478534\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1169597478538\" data-type=\"exercise\">\n<div id=\"fs-id1169597688446\" data-type=\"solution\">\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 12.1<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169597691022\" data-type=\"problem\">\n<p id=\"fs-id1169597533022\">Simplify: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-5d3783d2c55057d48d4a09ff4f3b68ed_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#56;&#123;&#97;&#125;&#94;&#123;&#45;&#52;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#94;&#123;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"26\" width=\"58\" style=\"vertical-align: -7px;\" \/>.<\/p>\n<\/div>\n<div data-type=\"solution\">\n<details>\n<summary>Show answer<\/summary>\n<p id=\"fs-id1169597533050\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-1a0d8b0f7a5fd645a0f21490676923a0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#54;&#52;&#125;&#123;&#123;&#97;&#125;&#94;&#123;&#56;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"23\" width=\"15\" style=\"vertical-align: -7px;\" \/><\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 12.2<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169597742767\" data-type=\"problem\">\n<p id=\"fs-id1169597742769\">Simplify: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-2c886a380174e559a3e1f06bbf1c57f2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#50;&#123;&#99;&#125;&#94;&#123;&#45;&#52;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#94;&#123;&#51;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"26\" width=\"56\" style=\"vertical-align: -7px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1169597742794\" data-type=\"solution\">\n<details>\n<summary>Show answer<\/summary>\n<p id=\"fs-id1169597742796\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-9d104c343a649fe84ee64314c369d72a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#56;&#125;&#123;&#123;&#99;&#125;&#94;&#123;&#49;&#50;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"23\" width=\"19\" style=\"vertical-align: -7px;\" \/><\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1169597533068\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1169597742764\" data-type=\"exercise\">\n<div id=\"fs-id1169597742767\" data-type=\"problem\">To simplify a fraction, we use the Quotient Property and subtract the exponents.<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--examples\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 13<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169597537035\" data-type=\"problem\">\n<p id=\"fs-id1169597537037\">Simplify: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-9dfdf04877cdddc9ad936d8ff71d6dd3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#123;&#114;&#125;&#94;&#123;&#53;&#125;&#125;&#123;&#123;&#114;&#125;&#94;&#123;&#45;&#52;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"26\" width=\"23\" style=\"vertical-align: -7px;\" \/>.<\/p>\n<\/div>\n<div data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<div data-type=\"title\">\n<table style=\"border-collapse: collapse;width: 100%\">\n<tbody>\n<tr>\n<td style=\"width: 50%\"><\/td>\n<td style=\"width: 50%\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-9dfdf04877cdddc9ad936d8ff71d6dd3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#123;&#114;&#125;&#94;&#123;&#53;&#125;&#125;&#123;&#123;&#114;&#125;&#94;&#123;&#45;&#52;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"26\" width=\"23\" style=\"vertical-align: -7px;\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%\">Use the Quotient Property, <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-b53c161692a009bf4009109559541202_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#123;&#97;&#125;&#94;&#123;&#109;&#125;&#125;&#123;&#123;&#97;&#125;&#94;&#123;&#110;&#125;&#125;&#61;&#123;&#97;&#125;&#94;&#123;&#109;&#45;&#110;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"23\" width=\"84\" style=\"vertical-align: -6px;\" \/>.<\/td>\n<td style=\"width: 50%\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-d8133a33eb90b6915df542e1ee44366b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#114;&#125;&#94;&#123;&#53;&#45;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#52;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"53\" style=\"vertical-align: 0px;\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%\">Simplify.<\/td>\n<td style=\"width: 50%\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-7251692fedacce639ca1fb315f23322b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#114;&#125;&#94;&#123;&#57;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"15\" style=\"vertical-align: 0px;\" \/><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 13.1<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169597740300\" data-type=\"problem\">\n<p id=\"fs-id1169597740302\">Simplify: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-1a27034a337557aceaab9db7e3a88805_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#123;&#120;&#125;&#94;&#123;&#56;&#125;&#125;&#123;&#123;&#120;&#125;&#94;&#123;&#45;&#51;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"26\" width=\"24\" style=\"vertical-align: -7px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1169597460929\" data-type=\"solution\">\n<details>\n<summary>Show answer<\/summary>\n<p id=\"fs-id1169597460931\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-3cd770a1ed1d1832580d94b7c0b90fc2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#120;&#125;&#94;&#123;&#49;&#49;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"23\" style=\"vertical-align: 0px;\" \/><\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 13.2<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div data-type=\"problem\">\n<p>Simplify: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-4bae54aeecafed41d59cc254fdf3f8b9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#123;&#121;&#125;&#94;&#123;&#56;&#125;&#125;&#123;&#123;&#121;&#125;&#94;&#123;&#45;&#54;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"30\" width=\"24\" style=\"vertical-align: -10px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1169597689448\" data-type=\"solution\">\n<details>\n<summary>Show answer<\/summary>\n<p id=\"fs-id1169597689450\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-49f57817947f8bbd06ceaecb7692eb3b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#121;&#125;&#94;&#123;&#49;&#52;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"23\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<h1>Convert from Decimal Notation to Scientific Notation<\/h1>\n<p id=\"fs-id1169597689470\">Remember working with place value for whole numbers and decimals? Our number system is based on powers of 10. We use tens, hundreds, thousands, and so on. Our decimal numbers are also based on powers of tens\u2014tenths, hundredths, thousandths, and so on. Consider the numbers 4,000 and <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-17e008f1bbd6c3846351523143d88b3d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#48;&#46;&#48;&#48;&#52;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"41\" style=\"vertical-align: 0px;\" \/>. We know that 4,000 means <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-754571bd569108e3c563d404e0086b23_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#52;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#105;&#109;&#101;&#115;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#49;&#44;&#48;&#48;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"81\" style=\"vertical-align: -4px;\" \/> and 0.004 means <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-bf0e4a29ba786eba378f3ba6277641b2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#52;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#105;&#109;&#101;&#115;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#49;&#44;&#48;&#48;&#48;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"25\" width=\"72\" style=\"vertical-align: -9px;\" \/>.<\/p>\n<p id=\"fs-id1169597740645\">If we write the 1000 as a power of ten in exponential form, we can rewrite these numbers in this way:<\/p>\n<div id=\"fs-id1169597740648\" class=\"unnumbered\" data-type=\"equation\" data-label=\"\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-b73e4d2f6273394ecafc1c692da536bc_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#98;&#101;&#103;&#105;&#110;&#123;&#97;&#114;&#114;&#97;&#121;&#125;&#123;&#99;&#99;&#99;&#99;&#125;&#52;&#44;&#48;&#48;&#48;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#38;&#32;&#38;&#32;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#52;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#48;&#46;&#48;&#48;&#52;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#92;&#32;&#52;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#105;&#109;&#101;&#115;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#49;&#44;&#48;&#48;&#48;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#38;&#32;&#38;&#32;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#52;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#52;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#105;&#109;&#101;&#115;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#49;&#44;&#48;&#48;&#48;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#92;&#32;&#52;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#105;&#109;&#101;&#115;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#123;&#49;&#48;&#125;&#94;&#123;&#51;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#38;&#32;&#38;&#32;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#52;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#52;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#105;&#109;&#101;&#115;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#123;&#49;&#48;&#125;&#94;&#123;&#51;&#125;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#92;&#32;&#38;&#32;&#38;&#32;&#38;&#32;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#52;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#52;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#105;&#109;&#101;&#115;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#123;&#49;&#48;&#125;&#94;&#123;&#45;&#51;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#101;&#110;&#100;&#123;&#97;&#114;&#114;&#97;&#121;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"80\" width=\"274\" style=\"vertical-align: -34px;\" \/><\/div>\n<p id=\"fs-id1169597742460\">In <em>scientific notation<\/em>, a number is expressed as the product of a coefficient and an exponential expression with a base of 10 and an integer power. The coefficient is a decimal number greater than or equal to 1 but less than 10, and the power of 10 is always an <strong>integer<\/strong>.<\/p>\n<div id=\"fs-id1169597742470\" data-type=\"note\">\n<div data-type=\"title\">\n<div class=\"textbox textbox--key-takeaways\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">Scientific Notation<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<p id=\"fs-id1169597742475\">A number is expressed in scientific notation when it is of the form<\/p>\n<div id=\"fs-id1169597742489\" class=\"unnumbered\" data-type=\"equation\" data-label=\"\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-68dc049a334c8433412aa71eb4e3229d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#98;&#101;&#103;&#105;&#110;&#123;&#97;&#114;&#114;&#97;&#121;&#125;&#123;&#99;&#99;&#99;&#99;&#125;&#38;&#32;&#38;&#32;&#38;&#32;&#97;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#105;&#109;&#101;&#115;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#123;&#49;&#48;&#125;&#94;&#123;&#110;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#119;&#104;&#101;&#114;&#101;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#49;&#92;&#108;&#101;&#32;&#97;&#60;&#49;&#48;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#97;&#110;&#100;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#110;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#105;&#115;&#32;&#97;&#110;&#32;&#105;&#110;&#116;&#101;&#103;&#101;&#114;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#101;&#110;&#100;&#123;&#97;&#114;&#114;&#97;&#121;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"346\" style=\"vertical-align: -4px;\" \/><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<p id=\"fs-id1169597516025\">It is customary in scientific notation to use as the <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-bd2900c84877f9303c3a37f124ed6fa2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#105;&#109;&#101;&#115;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"9\" width=\"10\" style=\"vertical-align: 0px;\" \/> multiplication sign, even though we avoid using this sign elsewhere in algebra.<\/p>\n<p id=\"fs-id1169597523393\">If we look at what happened to the decimal point, we can see a method to easily convert from decimal notation to <span class=\"no-emphasis\" data-type=\"term\">scientific notation<\/span>.<\/p>\n<p><span id=\"fs-id1169597523406\" data-type=\"media\" data-alt=\"This figure illustrates how to convert a number to scientific notation. It has two columns. In the first column is 4000 equals 4 times 10 to the third power. Below this, the equation is repeated, with an arrow demonstrating that the decimal point at the end of 4000 has moved three places to the left, so that 4000 becomes 4.000. The second column has 0.004 equals 4 times 10 to the negative third power. Below this, the equation is repeated, with an arrow demonstrating how the decimal point in 0.004 is moved three places to the right to produce 4.\"><img decoding=\"async\" class=\"aligncenter\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/uploads\/sites\/1441\/2021\/06\/CNX_ElemAlg_Figure_06_07_002_img_new.jpg\" alt=\"This figure illustrates how to convert a number to scientific notation. It has two columns. In the first column is 4000 equals 4 times 10 to the third power. Below this, the equation is repeated, with an arrow demonstrating that the decimal point at the end of 4000 has moved three places to the left, so that 4000 becomes 4.000. The second column has 0.004 equals 4 times 10 to the negative third power. Below this, the equation is repeated, with an arrow demonstrating how the decimal point in 0.004 is moved three places to the right to produce 4.\" data-media-type=\"image\/jpeg\" \/><\/span><\/p>\n<p id=\"fs-id1169597523423\">In both cases, the decimal was moved 3 places to get the coefficient between 1 and 10<\/p>\n<p id=\"fs-id1169594046599\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-e6b9a838b9511631627702cc4b7e0708_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#98;&#101;&#103;&#105;&#110;&#123;&#97;&#114;&#114;&#97;&#121;&#125;&#123;&#99;&#99;&#99;&#99;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#84;&#104;&#101;&#32;&#112;&#111;&#119;&#101;&#114;&#32;&#111;&#102;&#32;&#49;&#48;&#32;&#105;&#115;&#32;&#112;&#111;&#115;&#105;&#116;&#105;&#118;&#101;&#32;&#119;&#104;&#101;&#110;&#32;&#116;&#104;&#101;&#32;&#110;&#117;&#109;&#98;&#101;&#114;&#32;&#105;&#115;&#32;&#108;&#97;&#114;&#103;&#101;&#114;&#32;&#116;&#104;&#97;&#110;&#32;&#49;&#58;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#38;&#32;&#38;&#32;&#52;&#44;&#48;&#48;&#48;&#61;&#52;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#105;&#109;&#101;&#115;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#123;&#49;&#48;&#125;&#94;&#123;&#51;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#92;&#32;&#92;&#116;&#101;&#120;&#116;&#123;&#84;&#104;&#101;&#32;&#112;&#111;&#119;&#101;&#114;&#32;&#111;&#102;&#32;&#49;&#48;&#32;&#105;&#115;&#32;&#110;&#101;&#103;&#97;&#116;&#105;&#118;&#101;&#32;&#119;&#104;&#101;&#110;&#32;&#116;&#104;&#101;&#32;&#110;&#117;&#109;&#98;&#101;&#114;&#32;&#105;&#115;&#32;&#98;&#101;&#116;&#119;&#101;&#101;&#110;&#32;&#48;&#32;&#97;&#110;&#100;&#32;&#49;&#58;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#38;&#32;&#38;&#32;&#48;&#46;&#48;&#48;&#52;&#61;&#52;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#105;&#109;&#101;&#115;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#123;&#49;&#48;&#125;&#94;&#123;&#45;&#51;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#101;&#110;&#100;&#123;&#97;&#114;&#114;&#97;&#121;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"41\" width=\"696\" style=\"vertical-align: -15px;\" \/><\/p>\n<div class=\"textbox textbox--examples\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 14<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div data-type=\"title\">How to Convert from Decimal Notation to Scientific Notation<\/div>\n<div id=\"fs-id1169597691148\" data-type=\"exercise\">\n<div id=\"fs-id1169597691150\" data-type=\"problem\">\n<p id=\"fs-id1169597691152\">Write in scientific notation: 37,000.<\/p>\n<\/div>\n<div id=\"fs-id1169597691157\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<div data-type=\"title\">\n<table style=\"border-collapse: collapse;width: 100%\">\n<tbody>\n<tr>\n<td style=\"width: 59.4523%\">Step 1. Identify the decimal point&#8217;s current position in the number: In this case, the decimal point is after the last digit, so it&#8217;s located at the end of the number.<\/td>\n<td style=\"width: 40.5477%\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-eb121c1fc9b31ef58b1c31e3cbad67bc_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#51;&#55;&#44;&#48;&#48;&#48;&#32;&#92;&#99;&#111;&#108;&#111;&#114;&#123;&#114;&#101;&#100;&#125;&#123;&#92;&#115;&#99;&#97;&#108;&#101;&#98;&#111;&#120;&#123;&#50;&#125;&#123;&#46;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"57\" style=\"vertical-align: -4px;\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 59.4523%\">Step2. Count the number of places you need to move the decimal point to make the number between 1 and 10: In this case, you need to move the decimal point 4 places to the left.<\/td>\n<td style=\"width: 40.5477%\"><a href=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/uploads\/sites\/1441\/2021\/05\/Screenshot-2023-06-22-112012.jpg\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-2628\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/uploads\/sites\/1441\/2021\/05\/Screenshot-2023-06-22-112012.jpg\" alt=\"\" width=\"72\" height=\"64\" srcset=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/uploads\/sites\/1441\/2021\/05\/Screenshot-2023-06-22-112012.jpg 72w, https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/uploads\/sites\/1441\/2021\/05\/Screenshot-2023-06-22-112012-65x58.jpg 65w\" sizes=\"auto, (max-width: 72px) 100vw, 72px\" \/><\/a><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 59.4523%\">Step 3. Write the number as a decimal between 1 and 10, followed by the multiplication symbol<img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-326b1f7a6fdcbfa3500d0165b91b7369_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#32;&#40;&#92;&#116;&#105;&#109;&#101;&#115;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"26\" style=\"vertical-align: -5px;\" \/> and 10 raised to the power of the number of places the decimal point moved:<\/p>\n<ul>\n<li style=\"list-style-type: none\">\n<ul>\n<li>Decimal between 1 and 10: <strong>3.7<\/strong> (move the decimal point from 37000 four places to the left)<\/li>\n<li>Power of 10: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-9fe4ebab46e5fdb83e3555481d932abd_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#48;&#94;&#52;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"24\" style=\"vertical-align: 0px;\" \/><\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<\/td>\n<td style=\"width: 40.5477%\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-5c84ad99bc3d01d9f6547469996b72cf_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#51;&#46;&#55;&#32;&#92;&#116;&#105;&#109;&#101;&#115;&#32;&#49;&#48;&#94;&#123;&#52;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"69\" style=\"vertical-align: 0px;\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 59.4523%\">Step 4. Check: Check to see if your answer makes sense.<\/td>\n<td style=\"width: 40.5477%\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-9fe4ebab46e5fdb83e3555481d932abd_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#48;&#94;&#52;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"24\" style=\"vertical-align: 0px;\" \/> is 10,000<br \/>\nand<br \/>\n<img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-7923fa63e66f6be838f55d8158d7ece6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#48;&#44;&#48;&#48;&#48;&#32;&#92;&#116;&#105;&#109;&#101;&#115;&#32;&#51;&#46;&#55;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"96\" style=\"vertical-align: -4px;\" \/> will be <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-11cefd849deb0b25306465d0adb63209_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#51;&#55;&#44;&#48;&#48;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"53\" style=\"vertical-align: -4px;\" \/> .<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 14.1<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169597536011\" data-type=\"problem\">\n<p id=\"fs-id1169597536013\">Write in scientific notation: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-a5c9bdd7351b66542105fa030b31a8f0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#57;&#54;&#44;&#48;&#48;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"53\" style=\"vertical-align: -4px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1169597536022\" data-type=\"solution\">\n<details open=\"open\">\n<summary>Show answer<\/summary>\n<p id=\"fs-id1169597536024\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-2b6ac32479aa9cfe834604758e377837_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#57;&#46;&#54;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#105;&#109;&#101;&#115;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#123;&#49;&#48;&#125;&#94;&#123;&#52;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"76\" style=\"vertical-align: 0px;\" \/><\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 14.2<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169597536048\" data-type=\"problem\">\n<p id=\"fs-id1169597536050\">Write in scientific notation: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-9a72ec75973bf1ff4aa46365341f14b4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#52;&#56;&#44;&#51;&#48;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"53\" style=\"vertical-align: -4px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1169597536063\" data-type=\"solution\">\n<details open=\"open\">\n<summary>Show answer<\/summary>\n<p id=\"fs-id1169597701072\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-06922a1136c2ec4f0d8217a9e368ceeb_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#52;&#46;&#56;&#51;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#105;&#109;&#101;&#115;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#123;&#49;&#48;&#125;&#94;&#123;&#52;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"85\" style=\"vertical-align: 0px;\" \/><\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--key-takeaways\">\n<header class=\"textbox__header\">HOW TO: Convert from decimal notation to scientific notation<\/header>\n<div class=\"textbox__content\">\n<ol id=\"fs-id1168743403951\" class=\"stepwise\" type=\"1\">\n<li>Move the decimal point so that the first number is greater than or equal to 1 but less than 10.<\/li>\n<li>Count the number of decimal places, <em data-effect=\"italics\">n<\/em>, that the decimal point was moved.<\/li>\n<li>Write the number as a product with a power of 10.<br \/>\nIf the original number is:<\/p>\n<ul id=\"fs-id1168744092452\" data-bullet-style=\"bullet\">\n<li>greater than 1, the power of 10 will be 10<sup><em data-effect=\"italics\">n<\/em><\/sup>.<\/li>\n<li>between 0 and 1, the power of 10 will be 10<sup><em data-effect=\"italics\">\u2212n<\/em><\/sup>.<\/li>\n<\/ul>\n<\/li>\n<li>Check.<\/li>\n<\/ol>\n<\/div>\n<\/div>\n<div id=\"fs-id1168743403943\" class=\"howto\" data-type=\"note\">\n<div class=\"textbox textbox--examples\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 15<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169597701094\" data-type=\"problem\">\n<p id=\"fs-id1169597701096\">Write in scientific notation: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-d427f7a6c12448500fa00808d26d1dd5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#48;&#46;&#48;&#48;&#53;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"49\" style=\"vertical-align: 0px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1169597701105\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<div data-type=\"title\"><\/div>\n<p id=\"fs-id1169597701107\">The original number, <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-d427f7a6c12448500fa00808d26d1dd5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#48;&#46;&#48;&#48;&#53;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"49\" style=\"vertical-align: 0px;\" \/>, is between 0 and 1 so we will have a negative power of 10<\/p>\n<table style=\"border-collapse: collapse;width: 100%;height: 115px\">\n<tbody>\n<tr style=\"height: 25px\">\n<td style=\"width: 50%;height: 25px\"><\/td>\n<td style=\"width: 50%;height: 25px\"><span id=\"eip-id1172181050459\" data-type=\"media\" data-alt=\"0.0052.\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-638fdb05d03b1f3eb2984f1e88da3133_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#48;&#123;&#92;&#99;&#111;&#108;&#111;&#114;&#123;&#114;&#101;&#100;&#125;&#123;&#92;&#115;&#99;&#97;&#108;&#101;&#98;&#111;&#120;&#123;&#50;&#125;&#123;&#46;&#125;&#125;&#125;&#48;&#48;&#53;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"54\" style=\"vertical-align: 0px;\" \/><\/span><\/td>\n<\/tr>\n<tr style=\"height: 15px\">\n<td style=\"width: 50%;height: 15px\">Move the decimal point to get 5.2, a number between 1 and 10.<\/td>\n<td style=\"width: 50%;height: 15px\"><span id=\"eip-id1172181050475\" data-type=\"media\" data-alt=\"0.0052, with an arrow showing the decimal point jumping three places to the right until it ends up between the 5 and 2.\"><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/uploads\/sites\/1441\/2021\/06\/CNX_ElemAlg_Figure_06_07_004b_img_new.jpg\" alt=\"0.0052, with an arrow showing the decimal point jumping three places to the right until it ends up between the 5 and 2.\" width=\"119\" height=\"17\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr style=\"height: 15px\">\n<td style=\"width: 50%;height: 15px\">Count the number of decimal places the point was moved.<\/td>\n<td style=\"width: 50%;height: 15px\"><span id=\"eip-id1172181050492\" data-type=\"media\" data-alt=\"3 places.\">3 places<\/span><\/td>\n<\/tr>\n<tr style=\"height: 15px\">\n<td style=\"width: 50%;height: 15px\">Write as a product with a power of 10.<\/td>\n<td style=\"width: 50%;height: 15px\"><span id=\"eip-id1172181050509\" data-type=\"media\" data-alt=\"5.2 times 10 to the power of negative 3.\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-6abab9ae81021c010c837e6e70a2f919_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#53;&#46;&#50;&#32;&#92;&#116;&#105;&#109;&#101;&#115;&#32;&#49;&#48;&#94;&#123;&#45;&#51;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"80\" style=\"vertical-align: 0px;\" \/><\/span><\/td>\n<\/tr>\n<tr style=\"height: 15px\">\n<td style=\"width: 50%;height: 15px\">Check.<\/td>\n<td style=\"width: 50%;height: 15px\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-43d2106e3e55d4f19ac7b31871489117_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#98;&#101;&#103;&#105;&#110;&#123;&#97;&#114;&#114;&#97;&#121;&#125;&#123;&#99;&#99;&#99;&#99;&#99;&#125;&#92;&#92;&#32;&#92;&#92;&#32;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#51;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#53;&#46;&#50;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#105;&#109;&#101;&#115;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#123;&#49;&#48;&#125;&#94;&#123;&#45;&#51;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#92;&#32;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#51;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#61;&#53;&#46;&#50;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#105;&#109;&#101;&#115;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#123;&#49;&#48;&#125;&#94;&#123;&#51;&#125;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#92;&#32;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#51;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#61;&#53;&#46;&#50;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#105;&#109;&#101;&#115;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#49;&#48;&#48;&#48;&#125;&#32;&#92;&#92;&#32;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#51;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#61;&#53;&#46;&#50;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#105;&#109;&#101;&#115;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#48;&#46;&#48;&#48;&#49;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#92;&#32;&#92;&#40;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#50;&#32;&#101;&#109;&#125;&#123;&#48;&#32;&#101;&#120;&#125;&#125;&#61;&#48;&#46;&#48;&#48;&#53;&#50;&#32;&#92;&#99;&#104;&#101;&#99;&#107;&#109;&#97;&#114;&#107;&#32;&#92;&#101;&#110;&#100;&#123;&#97;&#114;&#114;&#97;&#121;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"105\" width=\"110\" style=\"vertical-align: -67px;\" \/><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 15.1<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169597577078\" data-type=\"problem\">\n<p id=\"fs-id1169597577080\">Write in scientific notation: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-5cf5c854e058547bdbf6b549a31443c8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#48;&#46;&#48;&#48;&#55;&#56;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"50\" style=\"vertical-align: 0px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1169597577089\" data-type=\"solution\">\n<details open=\"open\">\n<summary>Show answer<\/summary>\n<p id=\"fs-id1169597577091\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-e3bbd55578d2f88d660564827ae99076_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#55;&#46;&#56;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#105;&#109;&#101;&#115;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#123;&#49;&#48;&#125;&#94;&#123;&#45;&#51;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"87\" style=\"vertical-align: 0px;\" \/><\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1169597701126\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1169597577076\" data-type=\"exercise\">\n<div id=\"fs-id1169597577089\" data-type=\"solution\">\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 15.2<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169597577116\" data-type=\"problem\">\n<p id=\"fs-id1169597577118\">Write in scientific notation: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-eadbddf28e489794d8dffb0874aad948_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#48;&#46;&#48;&#49;&#50;&#57;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"50\" style=\"vertical-align: 0px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1169597577127\" data-type=\"solution\">\n<details open=\"open\">\n<summary>Show answer<\/summary>\n<p id=\"fs-id1169597555672\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-e033e1581c8768e9333fe27db4836cd3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#46;&#50;&#57;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#105;&#109;&#101;&#115;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#123;&#49;&#48;&#125;&#94;&#123;&#45;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"95\" style=\"vertical-align: 0px;\" \/><\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<h1>Convert Scientific Notation to Decimal Form<\/h1>\n<p id=\"fs-id1169597555698\">How can we convert from scientific notation to decimal form? Let\u2019s look at two numbers written in scientific notation and see.<\/p>\n<div id=\"fs-id1169597555702\" class=\"unnumbered\" data-type=\"equation\" data-label=\"\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-1426913cb64df866175ec8ca68b25060_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#98;&#101;&#103;&#105;&#110;&#123;&#97;&#114;&#114;&#97;&#121;&#125;&#123;&#99;&#99;&#99;&#99;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#57;&#46;&#49;&#50;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#105;&#109;&#101;&#115;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#123;&#49;&#48;&#125;&#94;&#123;&#52;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#38;&#32;&#38;&#32;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#52;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#57;&#46;&#49;&#50;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#105;&#109;&#101;&#115;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#123;&#49;&#48;&#125;&#94;&#123;&#45;&#52;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#92;&#32;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#57;&#46;&#49;&#50;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#105;&#109;&#101;&#115;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#49;&#48;&#44;&#48;&#48;&#48;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#38;&#32;&#38;&#32;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#52;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#57;&#46;&#49;&#50;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#105;&#109;&#101;&#115;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#48;&#46;&#48;&#48;&#48;&#49;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#92;&#32;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#57;&#49;&#44;&#50;&#48;&#48;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#38;&#32;&#38;&#32;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#52;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#48;&#46;&#48;&#48;&#48;&#57;&#49;&#50;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#101;&#110;&#100;&#123;&#97;&#114;&#114;&#97;&#121;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"63\" width=\"342\" style=\"vertical-align: -26px;\" \/><\/div>\n<p id=\"fs-id1169597688301\">If we look at the location of the decimal point, we can see an easy method to convert a number from scientific notation to decimal form.<\/p>\n<div class=\"unnumbered\" data-type=\"equation\" data-label=\"\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-a037f1c5cb75c4cb1bf30751b3de4c59_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#98;&#101;&#103;&#105;&#110;&#123;&#97;&#114;&#114;&#97;&#121;&#125;&#123;&#99;&#99;&#99;&#99;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#57;&#46;&#49;&#50;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#105;&#109;&#101;&#115;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#123;&#49;&#48;&#125;&#94;&#123;&#52;&#125;&#61;&#57;&#49;&#44;&#50;&#48;&#48;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#38;&#32;&#38;&#32;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#52;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#57;&#46;&#49;&#50;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#105;&#109;&#101;&#115;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#123;&#49;&#48;&#125;&#94;&#123;&#45;&#52;&#125;&#61;&#48;&#46;&#48;&#48;&#48;&#57;&#49;&#50;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#101;&#110;&#100;&#123;&#97;&#114;&#114;&#97;&#121;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"468\" style=\"vertical-align: -4px;\" \/><\/div>\n<p><span id=\"fs-id1169597742376\" data-type=\"media\" data-alt=\"This figure has two columns. In the left column is 9.12 times 10 to the fourth power equals 91,200. Below this, the same scientific notation is repeated, with an arrow showing the decimal point in 9.12 being moved four places to the right. Because there are no digits after 2, the final two places are represented by blank spaces. Below this is the text \u201cMove the decimal point four places to the right.\u201d In the right column is 9.12 times 10 to the negative fourth power equals 0.000912. Below this, the same scientific notation is repeated, with an arrow showing the decimal point in 9.12 being moved four places to the left. Because there are no digits before 9, the remaining three places are represented by spaces. Below this is the text \u201cMove the decimal point 4 places to the left.\u201d\"><img decoding=\"async\" class=\"aligncenter\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/uploads\/sites\/1441\/2021\/06\/CNX_ElemAlg_Figure_06_02_015_img.jpg\" alt=\"This figure has two columns. In the left column is 9.12 times 10 to the fourth power equals 91,200. Below this, the same scientific notation is repeated, with an arrow showing the decimal point in 9.12 being moved four places to the right. Because there are no digits after 2, the final two places are represented by blank spaces. Below this is the text \u201cMove the decimal point four places to the right.\u201d In the right column is 9.12 times 10 to the negative fourth power equals 0.000912. Below this, the same scientific notation is repeated, with an arrow showing the decimal point in 9.12 being moved four places to the left. Because there are no digits before 9, the remaining three places are represented by spaces. Below this is the text \u201cMove the decimal point 4 places to the left.\u201d\" data-media-type=\"image\/jpeg\" \/><\/span><\/p>\n<p id=\"fs-id1169597742371\">In both cases the decimal point moved 4 places. When the exponent was positive, the decimal moved to the right. When the exponent was negative, the decimal point moved to the left.<\/p>\n<div class=\"textbox textbox--examples\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 16<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div data-type=\"title\">How to Convert Scientific Notation to Decimal Form<\/div>\n<div id=\"fs-id1169597741743\" data-type=\"exercise\">\n<div id=\"fs-id1169597741745\" data-type=\"problem\">\n<p id=\"fs-id1169597741747\">Convert to decimal form: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-aa71f3eafd92c6a4863694f26dab6b0a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#54;&#46;&#50;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#105;&#109;&#101;&#115;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#123;&#49;&#48;&#125;&#94;&#123;&#51;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"76\" style=\"vertical-align: 0px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1169597741764\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<div data-type=\"title\">\n<table style=\"border-collapse: collapse;width: 100%;height: 149px\" data-alt=\"This figure is a table that has three columns and three rows. The first column is a header column, and it contains the names and numbers of each step. The second column contains further written instructions. The third column contains math. On the top row of the table, the first cell on the left reads \u201cStep 1. Determine the exponent, n, on the factor 10.\u201d The second cell reads \u201cThe exponent is 3.\u201d The third cell contains 6.2 times 10 cubed. In the second row, the first cell reads \u201cStep 2. Move the decimal n places, adding zeros if needed. If the exponent is positive, move the decimal point n places to the right. If the exponent is negative, move the decimal point absolute value of n places to the left.\u201d The second cell reads \u201cThe exponent is positive so move the decimal point 3 places to the right. We need to add two zeros as placeholders.\u201d The third cell contains 6.200, with an arrow showing the decimal point jumping places to the right, from between the 6 and 2 to after the second 00 in 6.200. Below this is the number 6,200. In the third row, the first cell reads \u201cStep 3. Check to see if your answer makes sense.\u201d The second cell is blank. The third reads \u201c10 cubed is 1000 and 1000 times 6.2 will be 6,200.\u201d Beneath this is 6.2 times 10 cubed equals 6,200.\">\n<tbody>\n<tr style=\"height: 33px\">\n<td style=\"width: 33.3333%;height: 33px\">Step 1. Determine the exponent, <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-1772f700b10cd40d7410781794beb211_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#110;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"11\" style=\"vertical-align: 0px;\" \/> on the factor <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-a0759639efdf9e489f10cac35a4e1850_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"17\" style=\"vertical-align: 0px;\" \/>.<\/td>\n<td style=\"width: 33.3333%;height: 33px\">The exponent is <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-4cf5983200020861d6bb094a2f1bf0ea_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#51;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"9\" style=\"vertical-align: 0px;\" \/>.<\/td>\n<td style=\"width: 33.3333%;height: 33px\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-10c4fd8f26b9c82395299871be2a921b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#54;&#46;&#50;&#32;&#92;&#116;&#105;&#109;&#101;&#115;&#32;&#49;&#48;&#94;&#51;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"69\" style=\"vertical-align: 0px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 116px\">\n<td style=\"width: 33.3333%;height: 116px\">\n<div>Step 2. Move the decimal <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-1772f700b10cd40d7410781794beb211_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#110;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"11\" style=\"vertical-align: 0px;\" \/> places, adding zeros if needed.<\/div>\n<div><\/div>\n<div>If the exponent is positive, move the decimal point <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-1772f700b10cd40d7410781794beb211_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#110;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"11\" style=\"vertical-align: 0px;\" \/> places to the right.<\/div>\n<div><\/div>\n<div>If the exponent is negative, move the decimal point <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-43e65b5124691682f445e713f788c5bf_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#32;&#124;&#110;&#124;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"17\" style=\"vertical-align: -5px;\" \/> places to the left.<\/div>\n<\/td>\n<td style=\"width: 33.3333%;height: 116px\">The exponent is positive, so move the decimal point 3 places to the right. We need to add 2 zeros as placeholders.<\/td>\n<td style=\"width: 33.3333%;height: 116px\"><a href=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/uploads\/sites\/1441\/2021\/05\/EX16_img1.jpg\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-2792\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/uploads\/sites\/1441\/2021\/05\/EX16_img1.jpg\" alt=\"\" width=\"56\" height=\"51\" \/><\/a> <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-cfbc42e71dc423c51225977fa7496b8b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#61;&#54;&#44;&#50;&#48;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"62\" style=\"vertical-align: -4px;\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 33.3333%\">\n<div>Step 3. Check to see if your answer makes sense.<\/div>\n<\/td>\n<td style=\"width: 33.3333%\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-1836842f5f5c0db749087f1fdca48f9a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#48;&#94;&#51;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"24\" style=\"vertical-align: 0px;\" \/> is <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-92c42062785f13e5efb05e33dac10ef6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#48;&#48;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"35\" style=\"vertical-align: 0px;\" \/> and <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-92c42062785f13e5efb05e33dac10ef6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#48;&#48;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"35\" style=\"vertical-align: 0px;\" \/> times <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-551876b231ac3bc85596b05dc994ab4b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#54;&#46;&#50;&#32;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"22\" style=\"vertical-align: 0px;\" \/> will be <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-77b47ac18ec8e2a7d9955bd5e0d055c8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#54;&#44;&#50;&#48;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"44\" style=\"vertical-align: -4px;\" \/>.<\/td>\n<td style=\"width: 33.3333%\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-f8d5463f1b7a10bffa97e4a675802e7d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#54;&#46;&#50;&#32;&#92;&#116;&#105;&#109;&#101;&#115;&#32;&#49;&#48;&#94;&#51;&#61;&#54;&#44;&#50;&#48;&#48;&#32;&#92;&#99;&#104;&#101;&#99;&#107;&#109;&#97;&#114;&#107;&#32;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"151\" style=\"vertical-align: -4px;\" \/><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 16.1<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169597741410\" data-type=\"problem\">\n<p id=\"fs-id1169597741412\">Convert to decimal form: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-32728f574639b4883988cb40601906b5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#46;&#51;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#105;&#109;&#101;&#115;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#123;&#49;&#48;&#125;&#94;&#123;&#51;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"75\" style=\"vertical-align: 0px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1169597741429\" data-type=\"solution\">\n<details open=\"open\">\n<summary>Show answer<\/summary>\n<p id=\"fs-id1169597741431\">1,300<\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1169597741404\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1169597741408\" data-type=\"exercise\">\n<div id=\"fs-id1169597741429\" data-type=\"solution\">\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 16.2<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169597741444\" data-type=\"problem\">\n<p id=\"fs-id1169597741446\">Convert to decimal form: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-fca5955c28e450ce614c0760c0c368f4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#57;&#46;&#50;&#53;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#105;&#109;&#101;&#115;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#123;&#49;&#48;&#125;&#94;&#123;&#52;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"85\" style=\"vertical-align: 0px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1169597505400\" data-type=\"solution\">\n<details open=\"open\">\n<summary>Show answer<\/summary>\n<p id=\"fs-id1169597505402\">92,500<\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<p id=\"fs-id1169597505408\">The steps are summarized below.<\/p>\n<div class=\"textbox textbox--key-takeaways\">\n<header class=\"textbox__header\">HOW TO: Convert scientific notation to decimal form.<\/header>\n<div class=\"textbox__content\">\n<p id=\"fs-id1169597505421\">To convert scientific notation to decimal form:<\/p>\n<ol id=\"fs-id1168746296183\" class=\"stepwise\" type=\"1\">\n<li>Identify the exponent, <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-1772f700b10cd40d7410781794beb211_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#110;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"11\" style=\"vertical-align: 0px;\" \/>, that represents the power of 10 in the scientific notation.<\/li>\n<li>Move the decimal <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-1772f700b10cd40d7410781794beb211_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#110;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"11\" style=\"vertical-align: 0px;\" \/> places, adding zeros if needed.\n<ul id=\"fs-id1169597505448\" data-bullet-style=\"bullet\">\n<li>If the exponent is positive, move the decimal point <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-1772f700b10cd40d7410781794beb211_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#110;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"11\" style=\"vertical-align: 0px;\" \/> places to the right.<\/li>\n<li>If the exponent is negative, move the decimal point <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-336b26eceb27421de4040de14a5aab68_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#124;&#110;&#124;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"17\" style=\"vertical-align: -5px;\" \/> places to the left.<\/li>\n<\/ul>\n<\/li>\n<li>Check.<\/li>\n<\/ol>\n<\/div>\n<\/div>\n<div id=\"fs-id1169597505412\" class=\"howto\" data-type=\"note\">\n<div class=\"textbox textbox--examples\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 17<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169597744324\" data-type=\"problem\">\n<p id=\"fs-id1169597744326\">Convert to decimal form: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-a1b83d5fc4fb485106915fe87b2a7b30_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#56;&#46;&#57;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#105;&#109;&#101;&#115;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#123;&#49;&#48;&#125;&#94;&#123;&#45;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"87\" style=\"vertical-align: 0px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1169597744344\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<table id=\"eip-id1172187383117\" class=\"unnumbered unstyled\" style=\"width: 100%\" summary=\"This figure has two columns. At the top of the figure, in the right column is 8.9 times 10 to the negative second power. One row down, the text in the left column says \u201cDetermine the exponent, n, on the factor 10.\u201d The right column says \u201cThe exponent is negative 2.\u201d One row down, the text in the left column says \u201cSince the exponent is negative, move the decimal point 2 places to the left.\u201d The right column contains 8.9, with an arrow showing the decimal point in 9.12 being moved two places to the left. Because there are no digits before 8, the remaining places are represented by spaces. One row down, the text in the left says \u201cAdd zeros as needed for placeholders.\u201d The right column contains 8.9 times 10 to the negative second power equals 0.089.\" data-label=\"\">\n<tbody>\n<tr>\n<td style=\"width: 60%\"><\/td>\n<td style=\"width: 40%\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-63f2e1d4b1f4dd178d37da39aeb7089b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#56;&#46;&#57;&#32;&#92;&#116;&#105;&#109;&#101;&#115;&#32;&#49;&#48;&#94;&#123;&#45;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"80\" style=\"vertical-align: 0px;\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 60%\">Identify the exponent, <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-1772f700b10cd40d7410781794beb211_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#110;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"11\" style=\"vertical-align: 0px;\" \/>, that represents the power of 10 in the scientific notation.<\/td>\n<td style=\"width: 40\">The exponent is <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-9df9cc12a240f44a2a90bf6f3d3fade8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"21\" style=\"vertical-align: 0px;\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 60%\">Since the exponent is negative, move the decimal point 2 places to the left.<\/td>\n<td style=\"width: 40%\"><span id=\"eip-id1172187383169\" data-type=\"media\" data-alt=\"8.9, with an arrow the decimal place showing the decimal point being moved two places to the left.\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/uploads\/sites\/1441\/2021\/06\/CNX_ElemAlg_Figure_06_07_007c_img_new.jpg\" alt=\"8.9, with an arrow the decimal place showing the decimal point being moved two places to the left.\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 60%\">Add zeros as needed for placeholders.<\/td>\n<td style=\"width: 40%\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-89b68032426a58aa5ac87f5c45915e81_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#56;&#46;&#57;&#32;&#92;&#116;&#105;&#109;&#101;&#115;&#32;&#49;&#48;&#94;&#123;&#45;&#50;&#125;&#32;&#61;&#32;&#48;&#46;&#48;&#56;&#57;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"145\" style=\"vertical-align: 0px;\" \/><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 17.1<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169597739737\" data-type=\"problem\">\n<p id=\"fs-id1169597739739\">Convert to decimal form: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-7b88611407c4e2ca205a87066a7354fa_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#46;&#50;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#105;&#109;&#101;&#115;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#123;&#49;&#48;&#125;&#94;&#123;&#45;&#52;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"86\" style=\"vertical-align: 0px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1169597739758\" data-type=\"solution\">\n<details open=\"open\">\n<summary>Show answer<\/summary>\n<p id=\"fs-id1169597739760\">0.00012<\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1169597744367\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1169597744371\" data-type=\"exercise\">\n<div id=\"fs-id1169597739758\" data-type=\"solution\">\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 17.2<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169597739772\" data-type=\"problem\">\n<p id=\"fs-id1169597739774\">Convert to decimal form: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-2ebb0f4e7c7f7b2522b7b90e8e3164b9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#55;&#46;&#53;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#105;&#109;&#101;&#115;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#123;&#49;&#48;&#125;&#94;&#123;&#45;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"87\" style=\"vertical-align: 0px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1169597739793\" data-type=\"solution\">\n<details open=\"open\">\n<summary>Show answer<\/summary>\n<p id=\"fs-id1169597739795\">0.075<\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<h1>Multiply and Divide Using Scientific Notation<\/h1>\n<p id=\"fs-id1169597704318\">Astronomers use very large numbers to describe distances in the universe and ages of stars and planets. Chemists use very small numbers to describe the size of an atom or the charge on an electron. When scientists perform calculations with very large or very small numbers, they use scientific notation. Scientific notation provides a way for the calculations to be done without writing a lot of zeros. We will see how the Properties of Exponents are used to multiply and divide numbers in scientific notation.<\/p>\n<div class=\"textbox textbox--examples\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 18<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169597704330\" data-type=\"problem\">\n<p id=\"fs-id1169597704332\">Multiply. Write answers in decimal form: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-994c69adf57ab18869e6c9547b664bbb_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#52;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#105;&#109;&#101;&#115;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#123;&#49;&#48;&#125;&#94;&#123;&#53;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#108;&#101;&#102;&#116;&#40;&#50;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#105;&#109;&#101;&#115;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#123;&#49;&#48;&#125;&#94;&#123;&#45;&#55;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"168\" style=\"vertical-align: -7px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1169597704374\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<div data-type=\"title\">\n<table style=\"border-collapse: collapse;width: 100%;height: 56px\">\n<tbody>\n<tr style=\"height: 14px\">\n<td style=\"width: 50%;height: 14px\"><\/td>\n<td style=\"width: 50%;height: 14px\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-25a8af151b333fe76a73dcf8a36e6fe7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#52;&#92;&#116;&#105;&#109;&#101;&#115;&#123;&#49;&#48;&#125;&#94;&#123;&#53;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#108;&#101;&#102;&#116;&#40;&#50;&#92;&#116;&#105;&#109;&#101;&#115;&#123;&#49;&#48;&#125;&#94;&#123;&#45;&#55;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"154\" style=\"vertical-align: -7px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 14px\">\n<td style=\"width: 50%;height: 14px\">Use the Commutative Property to rearrange the factors.<\/td>\n<td style=\"width: 50%;height: 14px\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-18cb4e76d617a497122e08af76c0b28d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#52;&#92;&#99;&#100;&#111;&#116;&#32;&#50;&#92;&#99;&#100;&#111;&#116;&#123;&#49;&#48;&#125;&#94;&#123;&#53;&#125;&#92;&#99;&#100;&#111;&#116;&#123;&#49;&#48;&#125;&#94;&#123;&#45;&#55;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"117\" style=\"vertical-align: 0px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 14px\">\n<td style=\"width: 50%;height: 14px\">Multiply.<\/td>\n<td style=\"width: 50%;height: 14px\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-8fde5f7a64f5cd473f236204b4c4d496_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#56;&#92;&#116;&#105;&#109;&#101;&#115;&#123;&#49;&#48;&#125;&#94;&#123;&#45;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"66\" style=\"vertical-align: 0px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 14px\">\n<td style=\"width: 50%;height: 14px\">Change to decimal form by moving the decimal two places left.<\/td>\n<td style=\"width: 50%;height: 14px\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-8020f49ba5eca15b88705f21ef5e1b24_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#48;&#46;&#48;&#56;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"32\" style=\"vertical-align: 0px;\" \/><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 18.1<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169597576869\" data-type=\"problem\">\n<p id=\"fs-id1169597576871\">Multiply <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-b00f73239febc5d95f34db2136a30b97_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#51;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#105;&#109;&#101;&#115;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#123;&#49;&#48;&#125;&#94;&#123;&#54;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#108;&#101;&#102;&#116;&#40;&#50;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#105;&#109;&#101;&#115;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#123;&#49;&#48;&#125;&#94;&#123;&#45;&#56;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"168\" style=\"vertical-align: -7px;\" \/>. Write answers in decimal form.<\/p>\n<\/div>\n<div id=\"fs-id1169597533136\" data-type=\"solution\">\n<details open=\"open\">\n<summary>Show answer<\/summary>\n<p id=\"fs-id1169597533139\">0.06<\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1169597576863\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1169597576867\" data-type=\"exercise\">\n<div id=\"fs-id1169597533136\" data-type=\"solution\">\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 18.2<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169597533151\" data-type=\"problem\">\n<p id=\"fs-id1169597533153\">Multiply <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-3676992301cd6431d905a9cf570d3272_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#51;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#105;&#109;&#101;&#115;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#123;&#49;&#48;&#125;&#94;&#123;&#45;&#50;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#108;&#101;&#102;&#116;&#40;&#51;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#105;&#109;&#101;&#115;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#123;&#49;&#48;&#125;&#94;&#123;&#45;&#49;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"179\" style=\"vertical-align: -7px;\" \/>. Write answers in decimal form.<\/p>\n<\/div>\n<div id=\"fs-id1169597705332\" data-type=\"solution\">\n<details open=\"open\">\n<summary>Show answer<\/summary>\n<p id=\"fs-id1169597705334\">0.009<\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1169597533145\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1169597533149\" data-type=\"exercise\">\n<div id=\"fs-id1169597705332\" data-type=\"solution\">\n<div class=\"textbox textbox--examples\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 19<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169597705345\" data-type=\"problem\">\n<p id=\"fs-id1169597705347\">Divide. Write answers in decimal form: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-c60d70d492f44445161706534c491d6c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#57;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#105;&#109;&#101;&#115;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#123;&#49;&#48;&#125;&#94;&#123;&#51;&#125;&#125;&#123;&#51;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#105;&#109;&#101;&#115;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#123;&#49;&#48;&#125;&#94;&#123;&#45;&#50;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"26\" width=\"55\" style=\"vertical-align: -7px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1169597705379\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<div data-type=\"title\">\n<table style=\"border-collapse: collapse;width: 100%\">\n<tbody>\n<tr>\n<td style=\"width: 50%\"><\/td>\n<td style=\"width: 50%\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-e5939f7b2b57e53f796019e693c1c524_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#57;&#92;&#116;&#105;&#109;&#101;&#115;&#123;&#49;&#48;&#125;&#94;&#123;&#51;&#125;&#125;&#123;&#51;&#92;&#116;&#105;&#109;&#101;&#115;&#123;&#49;&#48;&#125;&#94;&#123;&#45;&#50;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"26\" width=\"48\" style=\"vertical-align: -7px;\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%\">Rewrite as the product of two fractions.<\/td>\n<td style=\"width: 50%\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-54b56a9ba83301484458b5912d6c20ff_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#57;&#125;&#123;&#51;&#125;&#92;&#116;&#105;&#109;&#101;&#115;&#92;&#102;&#114;&#97;&#99;&#123;&#123;&#49;&#48;&#125;&#94;&#123;&#51;&#125;&#125;&#123;&#123;&#49;&#48;&#125;&#94;&#123;&#45;&#50;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"26\" width=\"62\" style=\"vertical-align: -7px;\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%\">Divide.<\/td>\n<td style=\"width: 50%\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-9921e975ec500f0633444d6b5dff1115_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#51;&#92;&#116;&#105;&#109;&#101;&#115;&#123;&#49;&#48;&#125;&#94;&#123;&#53;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"55\" style=\"vertical-align: 0px;\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%\">Change to decimal form by moving the decimal five places right.<\/td>\n<td style=\"width: 50%\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-048c1ba306c0ceca47898d52875dcb07_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#51;&#48;&#48;&#44;&#48;&#48;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"61\" style=\"vertical-align: -4px;\" \/><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 19.1<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169597539393\" data-type=\"problem\">\n<p id=\"fs-id1169597539395\">Divide <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-40dce46389ef5711b8e4e2e809d5e045_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#56;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#105;&#109;&#101;&#115;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#123;&#49;&#48;&#125;&#94;&#123;&#52;&#125;&#125;&#123;&#50;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#105;&#109;&#101;&#115;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#123;&#49;&#48;&#125;&#94;&#123;&#45;&#49;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"26\" width=\"55\" style=\"vertical-align: -7px;\" \/>. Write answers in decimal form.<\/p>\n<\/div>\n<div id=\"fs-id1169597539428\" data-type=\"solution\">\n<details open=\"open\">\n<summary>Show answer<\/summary>\n<p id=\"fs-id1169597539431\">400,000<\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 19.2<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169597539443\" data-type=\"problem\">\n<p id=\"fs-id1169597539445\">Divide <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-6bb05eace76ba5d653977149328f2446_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#56;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#105;&#109;&#101;&#115;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#123;&#49;&#48;&#125;&#94;&#123;&#50;&#125;&#125;&#123;&#52;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#105;&#109;&#101;&#115;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#123;&#49;&#48;&#125;&#94;&#123;&#45;&#50;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"26\" width=\"55\" style=\"vertical-align: -7px;\" \/>. Write answers in decimal form.<\/p>\n<\/div>\n<div id=\"fs-id1169597739980\" data-type=\"solution\">\n<details open=\"open\">\n<summary>Show answer<\/summary>\n<p id=\"fs-id1169597739982\">20,000<\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<p>Access these online resources for additional instruction and practice with integer exponents and scientific notation:<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1169597739988\" class=\"media-2\" data-type=\"note\">\n<ul id=\"fs-id1169597739997\" data-display=\"block\">\n<li><a href=\"https:\/\/openstax.org\/l\/25Negexponents\">Negative Exponents<\/a><\/li>\n<li><a href=\"https:\/\/openstax.org\/l\/25Scientnot1\">Scientific Notation<\/a><\/li>\n<li><a href=\"https:\/\/openstax.org\/l\/25Scientnot2\">Scientific Notation 2<\/a><\/li>\n<\/ul>\n<\/div>\n<h1>Key Concepts<\/h1>\n<ul id=\"fs-id1169597689120\" data-bullet-style=\"bullet\">\n<li><strong data-effect=\"bold\">Property of Negative Exponents<\/strong>\n<ul id=\"fs-id1169597689133\" data-bullet-style=\"open-circle\">\n<li>If <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-1772f700b10cd40d7410781794beb211_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#110;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"11\" style=\"vertical-align: 0px;\" \/> is a positive integer and <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-dfe13c0744369e0c0709de8599d9455f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#97;&#92;&#110;&#101;&#32;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"42\" style=\"vertical-align: -4px;\" \/>, then <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-864534955e4c36701312e28be58fec05_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#123;&#97;&#125;&#94;&#123;&#45;&#110;&#125;&#125;&#61;&#123;&#97;&#125;&#94;&#123;&#110;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"23\" width=\"67\" style=\"vertical-align: -7px;\" \/><\/li>\n<\/ul>\n<\/li>\n<li><strong data-effect=\"bold\">Quotient to a Negative Exponent<\/strong>\n<ul id=\"fs-id1169597689185\" data-bullet-style=\"open-circle\">\n<li>If <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-c8f07275913233044208899fc485a8ce_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#97;&#44;&#98;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"25\" style=\"vertical-align: -4px;\" \/> are real numbers, <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-9999f6afaa6cf08a5eae18617e31d237_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#98;&#92;&#110;&#101;&#32;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"40\" style=\"vertical-align: -4px;\" \/> and <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-1772f700b10cd40d7410781794beb211_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#110;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"11\" style=\"vertical-align: 0px;\" \/> is an integer , then <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-f03914d6346e9ed2526089212f9eeccd_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#92;&#102;&#114;&#97;&#99;&#123;&#97;&#125;&#123;&#98;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#94;&#123;&#45;&#110;&#125;&#61;&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#92;&#102;&#114;&#97;&#99;&#123;&#98;&#125;&#123;&#97;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#94;&#123;&#110;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"24\" width=\"104\" style=\"vertical-align: -7px;\" \/><\/li>\n<\/ul>\n<\/li>\n<li><strong data-effect=\"bold\">To convert a decimal to scientific notation:<\/strong>\n<ol id=\"fs-id1168746309069\" class=\"stepwise\" type=\"1\">\n<li>Move the decimal point so that the coefficient is greater than or equal to 1 but less than 10.<\/li>\n<li>Count the number of decimal places, <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-1772f700b10cd40d7410781794beb211_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#110;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"11\" style=\"vertical-align: 0px;\" \/>, that the decimal point was moved.<\/li>\n<li>Write the number as a product with a power of 10. If the original number is:\n<ul id=\"fs-id1169596704515\" data-bullet-style=\"open-circle\">\n<li>greater than 1, the power of 10 will be <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-0b17213f0337358d9cb59b3405ea79b7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#49;&#48;&#125;&#94;&#123;&#110;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"25\" style=\"vertical-align: 0px;\" \/><\/li>\n<li>between 0 and 1, the power of 10 will be <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-9e69264bab93ad5cb9e09b005c1c24dc_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#49;&#48;&#125;&#94;&#123;&#45;&#110;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"36\" style=\"vertical-align: 0px;\" \/><\/li>\n<\/ul>\n<\/li>\n<li>Check.<\/li>\n<\/ol>\n<\/li>\n<li><strong data-effect=\"bold\">To convert scientific notation to decimal form:<\/strong>\n<ol id=\"fs-id1168744116887\" class=\"stepwise\" type=\"1\">\n<li>Identify the exponent, denoted as <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-1772f700b10cd40d7410781794beb211_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#110;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"11\" style=\"vertical-align: 0px;\" \/>, that represents the power of 10 in the scientific notation.<\/li>\n<li>Move the decimal <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-1772f700b10cd40d7410781794beb211_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#110;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"11\" style=\"vertical-align: 0px;\" \/> places, adding zeros if needed.\n<ul id=\"fs-id1169597742509\" data-bullet-style=\"open-circle\">\n<li>If the exponent is positive, move the decimal point <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-1772f700b10cd40d7410781794beb211_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#110;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"11\" style=\"vertical-align: 0px;\" \/> places to the right.<\/li>\n<li>If the exponent is negative, move the decimal point <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-336b26eceb27421de4040de14a5aab68_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#124;&#110;&#124;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"17\" style=\"vertical-align: -5px;\" \/> places to the left.<\/li>\n<\/ul>\n<\/li>\n<li>Check<\/li>\n<\/ol>\n<\/li>\n<\/ul>\n<h1>Practice Makes Perfect<\/h1>\n<h2 id=\"fs-id1169597742555\" style=\"text-align: left\">Use the Definition of a Negative Exponent<\/h2>\n<p>In the following exercises, simplify.<\/p>\n<table style=\"border-collapse: collapse;width: 100%\">\n<tbody>\n<tr>\n<td style=\"width: 50.0893%\">\n<p id=\"fs-id1169597740962\">1. a) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-eeabe153fa94d5c20cbd61726431b41a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#51;&#125;&#94;&#123;&#45;&#52;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"27\" style=\"vertical-align: 0px;\" \/> b) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-45ae0e7ab3f3604f3ab2e07285dccaec_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#49;&#48;&#125;&#94;&#123;&#45;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"35\" style=\"vertical-align: 0px;\" \/><\/p>\n<\/td>\n<td style=\"width: 49.9107%\">\n<p id=\"fs-id1169597742567\">2. a) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-fa167090672f90743483dacbbdd005dc_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#52;&#125;&#94;&#123;&#45;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"27\" style=\"vertical-align: 0px;\" \/> b) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-eb0b6fc3c0e60a23266c29ed497c4f38_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#49;&#48;&#125;&#94;&#123;&#45;&#51;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"35\" style=\"vertical-align: 0px;\" \/><\/p>\n<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50.0893%\">\n<p id=\"fs-id1169597506410\">3. a) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-5a5bb36bb277d36dd8fab47e872ad9fe_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#50;&#125;&#94;&#123;&#45;&#56;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"27\" style=\"vertical-align: 0px;\" \/> b) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-45ae0e7ab3f3604f3ab2e07285dccaec_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#49;&#48;&#125;&#94;&#123;&#45;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"35\" style=\"vertical-align: 0px;\" \/><\/p>\n<\/td>\n<td style=\"width: 49.9107%\">4. a) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-533273505d05775e61c8acb93446896b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#53;&#125;&#94;&#123;&#45;&#51;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"27\" style=\"vertical-align: 0px;\" \/> b) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-fb64c0b6e9cb2ce529a04f7c6e0cb070_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#49;&#48;&#125;&#94;&#123;&#45;&#53;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"35\" style=\"vertical-align: 0px;\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50.0893%\">\n<p id=\"fs-id1169597741229\">5. a) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-9fdbbeefbbcc664ea115795915d639df_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#123;&#99;&#125;&#94;&#123;&#45;&#53;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"23\" width=\"23\" style=\"vertical-align: -7px;\" \/> b) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-97755a668a6d78711c3f8be929c8adfe_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#123;&#53;&#125;&#94;&#123;&#45;&#50;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"23\" width=\"23\" style=\"vertical-align: -7px;\" \/><\/p>\n<\/td>\n<td style=\"width: 49.9107%\">\n<p id=\"fs-id1169597741177\">6. a) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-9fdbbeefbbcc664ea115795915d639df_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#123;&#99;&#125;&#94;&#123;&#45;&#53;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"23\" width=\"23\" style=\"vertical-align: -7px;\" \/> b) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-6089359a69d0de84bd70e6e5f4d138af_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#123;&#51;&#125;&#94;&#123;&#45;&#50;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"23\" width=\"23\" style=\"vertical-align: -7px;\" \/><\/p>\n<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50.0893%\">\n<p id=\"fs-id1169597479428\">7. a) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-2e780a52d619488855ab609ef602f05a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#123;&#116;&#125;&#94;&#123;&#45;&#57;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"23\" width=\"22\" style=\"vertical-align: -7px;\" \/> b) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-677003bd31abfd3bbb0085bc891682b2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#123;&#49;&#48;&#125;&#94;&#123;&#45;&#52;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"23\" width=\"30\" style=\"vertical-align: -7px;\" \/><\/p>\n<\/td>\n<td style=\"width: 49.9107%\">\n<p id=\"fs-id1169597479374\">8. a) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-5b3ab297d573661db66c9730a536bb33_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#123;&#113;&#125;&#94;&#123;&#45;&#49;&#48;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"26\" width=\"29\" style=\"vertical-align: -10px;\" \/> b) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-0575d7f45b7dec56c4a6a648d697a453_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#123;&#49;&#48;&#125;&#94;&#123;&#45;&#51;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"23\" width=\"30\" style=\"vertical-align: -7px;\" \/><\/p>\n<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50.0893%\">\n<p id=\"fs-id1169597690713\">9. a) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-8ec8a2ef6978c6a4d5c984a78e5255da_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#92;&#102;&#114;&#97;&#99;&#123;&#51;&#125;&#123;&#49;&#48;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#94;&#123;&#45;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"26\" width=\"50\" style=\"vertical-align: -7px;\" \/> b) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-65115b7f577daf6a421c462aefa06a66_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#92;&#102;&#114;&#97;&#99;&#123;&#50;&#125;&#123;&#99;&#100;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#94;&#123;&#45;&#51;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"26\" width=\"63\" style=\"vertical-align: -7px;\" \/><\/p>\n<\/td>\n<td style=\"width: 49.9107%\">\n<p id=\"fs-id1169597539677\">10. a) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-9bc778e513def99abd782c6ab23fc83d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#92;&#102;&#114;&#97;&#99;&#123;&#53;&#125;&#123;&#56;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#94;&#123;&#45;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"26\" width=\"43\" style=\"vertical-align: -7px;\" \/> b) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-2dd85bed90b0a208be12cf6f15c56a50_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#92;&#102;&#114;&#97;&#99;&#123;&#51;&#109;&#125;&#123;&#110;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#94;&#123;&#45;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"26\" width=\"69\" style=\"vertical-align: -7px;\" \/><\/p>\n<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50.0893%\">\n<p id=\"fs-id1169597741526\">11. a)<img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-eb60854327151d15a0d0acc447a6c811_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#92;&#102;&#114;&#97;&#99;&#123;&#55;&#125;&#123;&#50;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#94;&#123;&#45;&#51;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"26\" width=\"43\" style=\"vertical-align: -7px;\" \/> b)<img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-a4c0f69b89c28c207e217c6a88144633_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#92;&#102;&#114;&#97;&#99;&#123;&#51;&#125;&#123;&#120;&#123;&#121;&#125;&#94;&#123;&#50;&#125;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#94;&#123;&#45;&#51;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"35\" width=\"76\" style=\"vertical-align: -11px;\" \/><\/p>\n<\/td>\n<td style=\"width: 49.9107%\">\n<p id=\"fs-id1169597741067\">12. a) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-d837f123fee6f83afff783f22e2f7106_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#92;&#102;&#114;&#97;&#99;&#123;&#52;&#125;&#123;&#57;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#94;&#123;&#45;&#51;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"26\" width=\"43\" style=\"vertical-align: -7px;\" \/> b) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-fe0df1b200d02101e92b34ee323c5a21_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#92;&#102;&#114;&#97;&#99;&#123;&#123;&#117;&#125;&#94;&#123;&#50;&#125;&#125;&#123;&#50;&#118;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#94;&#123;&#45;&#53;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"35\" width=\"69\" style=\"vertical-align: -11px;\" \/><\/p>\n<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50.0893%\">\n<p id=\"fs-id1169597702927\">13.<\/p>\n<p>a) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-bf3c1fa27b7c255e41ce62d187af35dc_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#55;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#94;&#123;&#45;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"53\" style=\"vertical-align: -5px;\" \/><br \/>\nb) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-cc229a9cb246c7cc81b4fe66ce272ea5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#123;&#55;&#125;&#94;&#123;&#45;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"40\" style=\"vertical-align: 0px;\" \/><br \/>\nc) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-571e0ab64342e9b566be3818f1ff9708_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#55;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#94;&#123;&#45;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"26\" width=\"57\" style=\"vertical-align: -7px;\" \/><br \/>\nd) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-1ffbb7774061cca34f8e3fa526260c22_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#55;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#94;&#123;&#45;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"26\" width=\"58\" style=\"vertical-align: -7px;\" \/><\/td>\n<td style=\"width: 49.9107%\">\n<p id=\"fs-id1169597741326\">14.<\/p>\n<p>a) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-543b6b927d60444409cb5a6aadbe8b55_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#53;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#94;&#123;&#45;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"53\" style=\"vertical-align: -5px;\" \/><br \/>\nb) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-135f5311f3f86fc939207ffa372eaf51_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#123;&#53;&#125;&#94;&#123;&#45;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"40\" style=\"vertical-align: 0px;\" \/><br \/>\nc) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-7b1dce0e48c52b7bc354cb8c0c735076_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#53;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#94;&#123;&#45;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"26\" width=\"57\" style=\"vertical-align: -7px;\" \/><br \/>\nd) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-8493b9625abd93b0482dbe719d7dd8ae_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#53;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#94;&#123;&#45;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"26\" width=\"58\" style=\"vertical-align: -7px;\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50.0893%\">\n<p id=\"fs-id1169597740612\">15.<\/p>\n<p>a) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-d4a105d6655587fb33b305e04d8a1fe9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#123;&#53;&#125;&#94;&#123;&#45;&#51;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"40\" style=\"vertical-align: 0px;\" \/><br \/>\nb) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-a898a42e641c2240a17e2eca78098800_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#53;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#94;&#123;&#45;&#51;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"26\" width=\"57\" style=\"vertical-align: -7px;\" \/><br \/>\nc) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-cb6200d9a68de9a74d59dcb23a067cf6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#53;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#94;&#123;&#45;&#51;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"26\" width=\"58\" style=\"vertical-align: -7px;\" \/><br \/>\nd) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-d86b8d6506b9951cab906a81907d2727_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#53;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#94;&#123;&#45;&#51;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"53\" style=\"vertical-align: -5px;\" \/><\/td>\n<td style=\"width: 49.9107%\">\n<p id=\"fs-id1169597742731\">16.<\/p>\n<p>a) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-4ba254d8b5541cd7615fdaefddc14d55_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#123;&#51;&#125;&#94;&#123;&#45;&#51;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"40\" style=\"vertical-align: 0px;\" \/><br \/>\nb) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-6c99cc5f96a1e67f35a355f3afcbf62d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#51;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#94;&#123;&#45;&#51;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"26\" width=\"57\" style=\"vertical-align: -7px;\" \/><br \/>\nc) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-7b66ab4ce18d35a4f3f8ff9ee61260d6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#51;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#94;&#123;&#45;&#51;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"26\" width=\"43\" style=\"vertical-align: -7px;\" \/><br \/>\nd) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-3553d394e540f4f80f977aa3b63733f7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#51;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#94;&#123;&#45;&#51;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"53\" style=\"vertical-align: -5px;\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50.0893%\">\n<p id=\"fs-id1169597518163\">17. a) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-34571345ec396deb74a31e95beb9aa77_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;&#92;&#99;&#100;&#111;&#116;&#123;&#53;&#125;&#94;&#123;&#45;&#49;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"48\" style=\"vertical-align: 0px;\" \/> b) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-4cdf5589a9394e0911bd7fbeb06038f5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#50;&#92;&#99;&#100;&#111;&#116;&#32;&#53;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#94;&#123;&#45;&#49;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"60\" style=\"vertical-align: -5px;\" \/><\/p>\n<\/td>\n<td style=\"width: 49.9107%\">\n<p id=\"fs-id1169597518095\">18. a) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-5fc2251ee8ccf3e08ac810f8ebddcf58_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#51;&#92;&#99;&#100;&#111;&#116;&#123;&#53;&#125;&#94;&#123;&#45;&#49;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"48\" style=\"vertical-align: 0px;\" \/> b) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-de0e19cdb19425444902bbcaf8e0fc6d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#51;&#92;&#99;&#100;&#111;&#116;&#32;&#53;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#94;&#123;&#45;&#49;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"60\" style=\"vertical-align: -5px;\" \/><\/p>\n<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50.0893%\">\n<p id=\"fs-id1169597517274\">19. a) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-0b8aff42540ba5431ec7b92311148e17_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#51;&#92;&#99;&#100;&#111;&#116;&#123;&#52;&#125;&#94;&#123;&#45;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"49\" style=\"vertical-align: 0px;\" \/> b) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-7be141d1c2433cd260afadecaa3045a6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#51;&#92;&#99;&#100;&#111;&#116;&#32;&#52;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#94;&#123;&#45;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"61\" style=\"vertical-align: -5px;\" \/><\/p>\n<\/td>\n<td style=\"width: 49.9107%\">\n<p id=\"fs-id1169597517205\">20. a) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-9d508d664a56bd3f901b45f5465b2fbb_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#52;&#92;&#99;&#100;&#111;&#116;&#123;&#53;&#125;&#94;&#123;&#45;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"49\" style=\"vertical-align: 0px;\" \/> b) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-6abad206fb8b75fce313772d75b33260_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#52;&#92;&#99;&#100;&#111;&#116;&#32;&#53;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#94;&#123;&#45;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"61\" style=\"vertical-align: -5px;\" \/><\/p>\n<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50.0893%\">\n<p id=\"fs-id1169597740316\">21. a) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-83e3a2b3a303c3ca1da5cde71172be10_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#98;&#125;&#94;&#123;&#45;&#53;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"26\" style=\"vertical-align: 0px;\" \/> b) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-ebdea64cd44942220fc43ac8e41109f1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#123;&#107;&#125;&#94;&#123;&#50;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#94;&#123;&#45;&#53;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"26\" width=\"50\" style=\"vertical-align: -7px;\" \/><\/p>\n<\/td>\n<td style=\"width: 49.9107%\">22. a) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-81db7168425652584bc8508bbf54006a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#109;&#125;&#94;&#123;&#45;&#52;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"34\" style=\"vertical-align: 0px;\" \/> b) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-aebb233fd648de944331ed7ba7a91461_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#123;&#120;&#125;&#94;&#123;&#51;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#94;&#123;&#45;&#52;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"26\" width=\"50\" style=\"vertical-align: -7px;\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50.0893%\">\n<p id=\"fs-id1169597742888\">23. a) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-d43fef539ab98e49d145340baaf5d262_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#115;&#125;&#94;&#123;&#45;&#56;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"26\" style=\"vertical-align: 0px;\" \/> b) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-7d26d25aabdc4d82919ce2fa458919c1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#123;&#97;&#125;&#94;&#123;&#57;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#94;&#123;&#45;&#49;&#48;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"26\" width=\"56\" style=\"vertical-align: -7px;\" \/><\/p>\n<\/td>\n<td style=\"width: 49.9107%\">24. a) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-ab0531de6c2243207d96135bcb9a4307_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#112;&#125;&#94;&#123;&#45;&#49;&#48;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"35\" style=\"vertical-align: -4px;\" \/> b) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-64c4bafb28ddc1a1dd2f672ad30df6f6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#123;&#113;&#125;&#94;&#123;&#54;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#94;&#123;&#45;&#56;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"26\" width=\"48\" style=\"vertical-align: -7px;\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50.0893%\">\n<p id=\"fs-id1169597742094\">25.<\/p>\n<p>a) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-c23b95f91e64d5d49acfdba62d1c2b9d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#54;&#123;&#114;&#125;&#94;&#123;&#45;&#49;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"34\" style=\"vertical-align: 0px;\" \/><br \/>\nb) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-a60115cbe68a65465a0b2444a6bdfe92_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#54;&#114;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#94;&#123;&#45;&#49;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"47\" style=\"vertical-align: -5px;\" \/><br \/>\nc) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-dd412d0e6715ad315f8601016ee3908f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#54;&#114;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#94;&#123;&#45;&#49;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"61\" style=\"vertical-align: -5px;\" \/><\/td>\n<td style=\"width: 49.9107%\">\n<p id=\"fs-id1169597742959\">26.<\/p>\n<p>a) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-7f9a81ba260460bf42c3b2e7d7eb912d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#55;&#123;&#110;&#125;&#94;&#123;&#45;&#49;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"37\" style=\"vertical-align: 0px;\" \/><br \/>\nb) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-2fa97e2d4357abf8477c5288fb5f9fca_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#55;&#110;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#94;&#123;&#45;&#49;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"49\" style=\"vertical-align: -5px;\" \/><br \/>\nc) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-75ab2229d7ac0acf42525dc9d1900315_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#55;&#110;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#94;&#123;&#45;&#49;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"63\" style=\"vertical-align: -5px;\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50.0893%\">\n<p id=\"fs-id1169597703627\">27.<\/p>\n<p>a) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-c2e6ea83175af965bdf635d87014851a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#50;&#113;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#94;&#123;&#45;&#52;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"48\" style=\"vertical-align: -5px;\" \/><br \/>\nb) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-7568fff621545df30398a5b73bfb45e1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;&#123;&#113;&#125;&#94;&#123;&#45;&#52;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"35\" style=\"vertical-align: -4px;\" \/><br \/>\nc) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-c3f83cc548ea3a594392b6dfee718b84_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#50;&#123;&#113;&#125;&#94;&#123;&#45;&#52;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"48\" style=\"vertical-align: -4px;\" \/><\/td>\n<td style=\"width: 49.9107%\">\n<p id=\"fs-id1169597441155\">28.<\/p>\n<p>a) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-56ce5287bc25c13196f9999afd0baef3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#51;&#112;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#94;&#123;&#45;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"49\" style=\"vertical-align: -5px;\" \/><br \/>\nb) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-7f6befba9d1e1829e3daec0b4c349514_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#51;&#123;&#112;&#125;&#94;&#123;&#45;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"36\" style=\"vertical-align: -4px;\" \/><br \/>\nc) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-7628e3042d8627bfc542a67a69e4b7cb_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#51;&#123;&#112;&#125;&#94;&#123;&#45;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"49\" style=\"vertical-align: -4px;\" \/><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<h2 id=\"fs-id1169597740795\" style=\"text-align: left\">Simplify Expressions with Integer Exponents<\/h2>\n<p>In the following exercises, simplify.<\/p>\n<table style=\"border-collapse: collapse;width: 100%;height: 293px\">\n<tbody>\n<tr style=\"height: 94px\">\n<td style=\"width: 50%;height: 94px\">\n<p id=\"fs-id1169597740903\">29.<\/p>\n<p>a) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-01bc720605ef2e8f3930c40e554d9710_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#115;&#125;&#94;&#123;&#51;&#125;&#92;&#99;&#100;&#111;&#116;&#123;&#115;&#125;&#94;&#123;&#45;&#55;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"55\" style=\"vertical-align: 0px;\" \/><br \/>\nb) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-d6687cb1679743f61eb2994e845f27c9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#113;&#125;&#94;&#123;&#45;&#56;&#125;&#92;&#99;&#100;&#111;&#116;&#123;&#113;&#125;&#94;&#123;&#51;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"55\" style=\"vertical-align: -4px;\" \/><br \/>\nc) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-c421d2117f627298ca7a986dabf5ab2c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#121;&#125;&#94;&#123;&#45;&#50;&#125;&#92;&#99;&#100;&#111;&#116;&#123;&#121;&#125;&#94;&#123;&#45;&#53;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"68\" style=\"vertical-align: -4px;\" \/><\/td>\n<td style=\"width: 50%;height: 94px\">30.<\/p>\n<p>a) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-b574959c203fbba6050410a3d730e214_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#98;&#125;&#94;&#123;&#52;&#125;&#123;&#98;&#125;&#94;&#123;&#45;&#56;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"41\" style=\"vertical-align: 0px;\" \/><br \/>\nb) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-2e7e1cb1ab5b33b02d234fa057070684_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#114;&#125;&#94;&#123;&#45;&#50;&#125;&#123;&#114;&#125;&#94;&#123;&#53;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"42\" style=\"vertical-align: 0px;\" \/><br \/>\nc) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-2127bf4d3fe1cfb44a99d113c3e8ab44_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#120;&#125;&#94;&#123;&#45;&#55;&#125;&#123;&#120;&#125;&#94;&#123;&#45;&#51;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"57\" style=\"vertical-align: 0px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 94px\">\n<td style=\"width: 50%;height: 94px\">\n<p id=\"fs-id1169597740082\">31.<\/p>\n<p>a) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-a118e1e5819cdef1e2c1a7a60a172e0f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#121;&#125;&#94;&#123;&#53;&#125;&#92;&#99;&#100;&#111;&#116;&#123;&#121;&#125;&#94;&#123;&#45;&#53;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"57\" style=\"vertical-align: -4px;\" \/><br \/>\nb) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-7aa38e9ee7617a56bcf8e5d548565b76_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#92;&#99;&#100;&#111;&#116;&#123;&#121;&#125;&#94;&#123;&#53;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"38\" style=\"vertical-align: -4px;\" \/><br \/>\nc) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-398599c6369ca3e8a440cacde54d301e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#92;&#99;&#100;&#111;&#116;&#123;&#121;&#125;&#94;&#123;&#45;&#53;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"49\" style=\"vertical-align: -4px;\" \/><\/td>\n<td style=\"width: 50%;height: 94px\">\n<p id=\"fs-id1169597701723\">32.<\/p>\n<p>a) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-1bbf48687b2b4a7347f186a4f2614f63_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#97;&#125;&#94;&#123;&#51;&#125;&#92;&#99;&#100;&#111;&#116;&#123;&#97;&#125;&#94;&#123;&#45;&#51;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"57\" style=\"vertical-align: 0px;\" \/><br \/>\nb) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-218ab887a9c0db37e0ece949ab8886ff_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#97;&#92;&#99;&#100;&#111;&#116;&#123;&#97;&#125;&#94;&#123;&#51;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"38\" style=\"vertical-align: 0px;\" \/><br \/>\nc) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-6c29cbd7ff8e94cb8c2bd8a192f6450f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#97;&#92;&#99;&#100;&#111;&#116;&#123;&#97;&#125;&#94;&#123;&#45;&#51;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"49\" style=\"vertical-align: 0px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 15px\">\n<td style=\"width: 50%;height: 15px\">33. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-0b883e338a9a331c3edea84a8b71c893_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#120;&#125;&#94;&#123;&#52;&#125;&#92;&#99;&#100;&#111;&#116;&#123;&#120;&#125;&#94;&#123;&#45;&#50;&#125;&#92;&#99;&#100;&#111;&#116;&#123;&#120;&#125;&#94;&#123;&#45;&#51;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"100\" style=\"vertical-align: 0px;\" \/><\/td>\n<td style=\"width: 50%;height: 15px\">34. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-ef90514d9b4c53500db0b25a9f228735_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#123;&#119;&#125;&#94;&#123;&#52;&#125;&#123;&#120;&#125;&#94;&#123;&#45;&#53;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#108;&#101;&#102;&#116;&#40;&#123;&#119;&#125;&#94;&#123;&#45;&#50;&#125;&#123;&#120;&#125;&#94;&#123;&#45;&#52;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"141\" style=\"vertical-align: -7px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 15px\">\n<td style=\"width: 50%;height: 15px\">35. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-c76ef85915cccc7626e1c979204634d0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#123;&#109;&#125;&#94;&#123;&#51;&#125;&#123;&#110;&#125;&#94;&#123;&#45;&#51;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#108;&#101;&#102;&#116;&#40;&#123;&#109;&#125;&#94;&#123;&#45;&#53;&#125;&#123;&#110;&#125;&#94;&#123;&#45;&#49;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"147\" style=\"vertical-align: -7px;\" \/><\/td>\n<td style=\"width: 50%;height: 15px\">36. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-09016be0f35775c1588ba133312948c1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#117;&#123;&#118;&#125;&#94;&#123;&#45;&#50;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#108;&#101;&#102;&#116;&#40;&#123;&#117;&#125;&#94;&#123;&#45;&#53;&#125;&#123;&#118;&#125;&#94;&#123;&#45;&#51;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"125\" style=\"vertical-align: -7px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 15px\">\n<td style=\"width: 50%;height: 15px\">37. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-94571e2c2f6fa84f79969b94e06e35d5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#112;&#123;&#113;&#125;&#94;&#123;&#45;&#52;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#108;&#101;&#102;&#116;&#40;&#123;&#112;&#125;&#94;&#123;&#45;&#54;&#125;&#123;&#113;&#125;&#94;&#123;&#45;&#51;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"121\" style=\"vertical-align: -7px;\" \/><\/td>\n<td style=\"width: 50%;height: 15px\">38. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-1b7fdde632af1fdd7dc34087531fe00a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#54;&#123;&#99;&#125;&#94;&#123;&#45;&#51;&#125;&#123;&#100;&#125;&#94;&#123;&#57;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#108;&#101;&#102;&#116;&#40;&#50;&#123;&#99;&#125;&#94;&#123;&#52;&#125;&#123;&#100;&#125;&#94;&#123;&#45;&#53;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"149\" style=\"vertical-align: -7px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 15px\">\n<td style=\"width: 50%;height: 15px\">39. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-90458ebdfb11fc43085bf432ff2e085f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#50;&#123;&#106;&#125;&#94;&#123;&#45;&#53;&#125;&#123;&#107;&#125;&#94;&#123;&#56;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#108;&#101;&#102;&#116;&#40;&#55;&#123;&#106;&#125;&#94;&#123;&#50;&#125;&#123;&#107;&#125;&#94;&#123;&#45;&#51;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"151\" style=\"vertical-align: -7px;\" \/><\/td>\n<td style=\"width: 50%;height: 15px\">40. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-2d6806c2ce7456c913b11320fced4a08_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#52;&#123;&#114;&#125;&#94;&#123;&#45;&#50;&#125;&#123;&#115;&#125;&#94;&#123;&#45;&#56;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#108;&#101;&#102;&#116;&#40;&#57;&#123;&#114;&#125;&#94;&#123;&#52;&#125;&#123;&#115;&#125;&#94;&#123;&#51;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"149\" style=\"vertical-align: -7px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 15px\">\n<td style=\"width: 50%;height: 15px\">41. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-5d894acde0840f069df25ebacf3aae6a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#53;&#123;&#109;&#125;&#94;&#123;&#52;&#125;&#123;&#110;&#125;&#94;&#123;&#54;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#108;&#101;&#102;&#116;&#40;&#56;&#123;&#109;&#125;&#94;&#123;&#45;&#53;&#125;&#123;&#110;&#125;&#94;&#123;&#45;&#51;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"167\" style=\"vertical-align: -7px;\" \/><\/td>\n<td style=\"width: 50%;height: 15px\">42. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-0dda776be9d33aea0b13c3dab0ddff89_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#53;&#123;&#120;&#125;&#94;&#123;&#50;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#94;&#123;&#45;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"26\" width=\"59\" style=\"vertical-align: -7px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 15px\">\n<td style=\"width: 50%;height: 15px\">43. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-d97a2acc9ddc09f05f359e1ef050823f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#52;&#123;&#121;&#125;&#94;&#123;&#51;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#94;&#123;&#45;&#51;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"26\" width=\"58\" style=\"vertical-align: -7px;\" \/><\/td>\n<td style=\"width: 50%;height: 15px\">44. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-df0d5d39c1848bc6947226f843366dd8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#51;&#123;&#122;&#125;&#94;&#123;&#45;&#51;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#94;&#123;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"26\" width=\"58\" style=\"vertical-align: -7px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 15px\">\n<td style=\"width: 50%;height: 15px\">45. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-9acde1e4abca1201598a37740df3acb8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#50;&#123;&#112;&#125;&#94;&#123;&#45;&#53;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#94;&#123;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"26\" width=\"57\" style=\"vertical-align: -7px;\" \/><\/td>\n<td style=\"width: 50%;height: 15px\">46. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-cbf68e822e6fa64e4433b59fd0ea2d8a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#123;&#116;&#125;&#94;&#123;&#57;&#125;&#125;&#123;&#123;&#116;&#125;&#94;&#123;&#45;&#51;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"26\" width=\"22\" style=\"vertical-align: -7px;\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%\">47. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-cbe18b125aaa728bcac5341b7011047e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#123;&#110;&#125;&#94;&#123;&#53;&#125;&#125;&#123;&#123;&#110;&#125;&#94;&#123;&#45;&#50;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"26\" width=\"25\" style=\"vertical-align: -7px;\" \/><\/td>\n<td style=\"width: 50%\">48. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-8f1e540b63f2dba89fddb252b2a09198_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#123;&#120;&#125;&#94;&#123;&#45;&#55;&#125;&#125;&#123;&#123;&#120;&#125;&#94;&#123;&#45;&#51;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"26\" width=\"24\" style=\"vertical-align: -7px;\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%\">49. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-efdf8bce07e8191f383f2de40c09d4a0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#123;&#121;&#125;&#94;&#123;&#45;&#53;&#125;&#125;&#123;&#123;&#121;&#125;&#94;&#123;&#45;&#49;&#48;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"30\" width=\"30\" style=\"vertical-align: -10px;\" \/><\/td>\n<td style=\"width: 50%\"><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<h2 id=\"fs-id1169597726176\" style=\"text-align: left\">Convert from Decimal Notation to Scientific Notation<\/h2>\n<p id=\"fs-id1168746687025\">In the following exercises, write each number in scientific notation.<\/p>\n<table style=\"border-collapse: collapse;width: 100%\">\n<tbody>\n<tr>\n<td style=\"width: 50%\">50. 57,000<\/td>\n<td style=\"width: 50%\">51. 340,000<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%\">52. 8,750,000<\/td>\n<td style=\"width: 50%\">53. 1,290,000<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%\">54. 0.026<\/td>\n<td style=\"width: 50%\">55. 0.041<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%\">56. 0.00000871<\/td>\n<td style=\"width: 50%\">57. 0.00000103<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<h2 id=\"fs-id1169597739266\" style=\"text-align: left\">Convert Scientific Notation to Decimal Form<\/h2>\n<p id=\"fs-id1168744093748\">In the following exercises, convert each number to decimal form.<\/p>\n<table style=\"border-collapse: collapse;width: 100%\">\n<tbody>\n<tr>\n<td style=\"width: 50%\">58. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-4688e33a8b535fdb9378ccc9c2b19294_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#53;&#46;&#50;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#105;&#109;&#101;&#115;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#123;&#49;&#48;&#125;&#94;&#123;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"76\" style=\"vertical-align: 0px;\" \/><\/td>\n<td style=\"width: 50%\">59. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-822d8f14d5b62325190b1c5b5981af16_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#56;&#46;&#51;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#105;&#109;&#101;&#115;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#123;&#49;&#48;&#125;&#94;&#123;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"76\" style=\"vertical-align: 0px;\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%\">60. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-de069a853c6c27f8766998d90ee070e2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#55;&#46;&#53;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#105;&#109;&#101;&#115;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#123;&#49;&#48;&#125;&#94;&#123;&#54;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"76\" style=\"vertical-align: 0px;\" \/><\/td>\n<td style=\"width: 50%\">61. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-7f41da0fe012f89fcf5b359e9400d337_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#46;&#54;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#105;&#109;&#101;&#115;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#123;&#49;&#48;&#125;&#94;&#123;&#49;&#48;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"82\" style=\"vertical-align: 0px;\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%\">62. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-c1c2165d2b6e1458af6534568b411c34_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;&#46;&#53;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#105;&#109;&#101;&#115;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#123;&#49;&#48;&#125;&#94;&#123;&#45;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"87\" style=\"vertical-align: 0px;\" \/><\/td>\n<td style=\"width: 50%\">63. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-f71b41934676a1b8a91b659fb76deee9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#51;&#46;&#56;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#105;&#109;&#101;&#115;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#123;&#49;&#48;&#125;&#94;&#123;&#45;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"87\" style=\"vertical-align: 0px;\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%\">64. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-95bed9c3a778677233b91c386a4e8790_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#52;&#46;&#49;&#51;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#105;&#109;&#101;&#115;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#123;&#49;&#48;&#125;&#94;&#123;&#45;&#53;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"96\" style=\"vertical-align: 0px;\" \/><\/td>\n<td style=\"width: 50%\">65. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-b2bedc30d64f7a967bb40e150aad1610_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#46;&#57;&#51;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#105;&#109;&#101;&#115;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#123;&#49;&#48;&#125;&#94;&#123;&#45;&#53;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"95\" style=\"vertical-align: 0px;\" \/><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<h2 id=\"fs-id1169597702129\" style=\"text-align: left\">Multiply and Divide Using Scientific Notation<\/h2>\n<p id=\"fs-id1168746297450\">In the following exercises, multiply. Write your answer in decimal form.<\/p>\n<table style=\"border-collapse: collapse;width: 100%\">\n<tbody>\n<tr>\n<td style=\"width: 50%\">66. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-4b286fce3bf097bc59ba1f446a452c2f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#51;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#105;&#109;&#101;&#115;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#123;&#49;&#48;&#125;&#94;&#123;&#45;&#53;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#108;&#101;&#102;&#116;&#40;&#51;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#105;&#109;&#101;&#115;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#123;&#49;&#48;&#125;&#94;&#123;&#57;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"168\" style=\"vertical-align: -7px;\" \/><\/td>\n<td style=\"width: 50%\">67. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-4b56a400035f5bb8eac2963f27d84ffc_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#50;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#105;&#109;&#101;&#115;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#123;&#49;&#48;&#125;&#94;&#123;&#50;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#108;&#101;&#102;&#116;&#40;&#49;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#105;&#109;&#101;&#115;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#123;&#49;&#48;&#125;&#94;&#123;&#45;&#52;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"168\" style=\"vertical-align: -7px;\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%\">68. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-199f5b9d79701e158a9c09d5c26cd575_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#55;&#46;&#49;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#105;&#109;&#101;&#115;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#123;&#49;&#48;&#125;&#94;&#123;&#45;&#50;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#108;&#101;&#102;&#116;&#40;&#50;&#46;&#52;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#105;&#109;&#101;&#115;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#123;&#49;&#48;&#125;&#94;&#123;&#45;&#52;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"206\" style=\"vertical-align: -7px;\" \/><\/td>\n<td style=\"width: 50%\">69. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-e5ee3d10ec4af19c54e78b4d507acac6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#51;&#46;&#53;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#105;&#109;&#101;&#115;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#123;&#49;&#48;&#125;&#94;&#123;&#45;&#52;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#108;&#101;&#102;&#116;&#40;&#49;&#46;&#54;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#105;&#109;&#101;&#115;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#123;&#49;&#48;&#125;&#94;&#123;&#45;&#50;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"206\" style=\"vertical-align: -7px;\" \/><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p id=\"fs-id1169597537502\">In the following exercises, divide. Write your answer in decimal form.<\/p>\n<table style=\"border-collapse: collapse;width: 100%\">\n<tbody>\n<tr>\n<td style=\"width: 50%\">70. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-c9496fe53fe3017f77c3f2c0cef92583_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#55;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#105;&#109;&#101;&#115;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#123;&#49;&#48;&#125;&#94;&#123;&#45;&#51;&#125;&#125;&#123;&#49;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#105;&#109;&#101;&#115;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#123;&#49;&#48;&#125;&#94;&#123;&#45;&#55;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"26\" width=\"55\" style=\"vertical-align: -7px;\" \/><\/td>\n<td style=\"width: 50%\">71. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-ee4f11e7e4aca9df8b968c96bfce400c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#53;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#105;&#109;&#101;&#115;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#123;&#49;&#48;&#125;&#94;&#123;&#45;&#50;&#125;&#125;&#123;&#49;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#105;&#109;&#101;&#115;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#123;&#49;&#48;&#125;&#94;&#123;&#45;&#49;&#48;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"26\" width=\"61\" style=\"vertical-align: -7px;\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%\">72. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-ad5fcece639145ad9ae2df377a8ed657_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#54;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#105;&#109;&#101;&#115;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#123;&#49;&#48;&#125;&#94;&#123;&#52;&#125;&#125;&#123;&#51;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#105;&#109;&#101;&#115;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#123;&#49;&#48;&#125;&#94;&#123;&#45;&#50;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"26\" width=\"55\" style=\"vertical-align: -7px;\" \/><\/td>\n<td style=\"width: 50%\">73. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-e53e3f53050c20faeebb7d5e4e77dea8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#56;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#105;&#109;&#101;&#115;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#123;&#49;&#48;&#125;&#94;&#123;&#54;&#125;&#125;&#123;&#52;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#105;&#109;&#101;&#115;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#123;&#49;&#48;&#125;&#94;&#123;&#45;&#49;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"26\" width=\"55\" style=\"vertical-align: -7px;\" \/><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<h2 style=\"text-align: left\" data-type=\"title\">Everyday Math<\/h2>\n<table style=\"border-collapse: collapse;width: 100%\">\n<tbody>\n<tr>\n<td style=\"width: 50%\">74. The population of the United States on July 1, 2010 was about 34,000,000. Write the number in scientific notation.<\/td>\n<td style=\"width: 50%\">75. The population of the world on July 1, 2010 was more than 6,850,000,000. Write the number in scientific notation<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%\">76. The average width of a human hair is 0.0018 centimetres. Write the number in scientific notation.<\/td>\n<td style=\"width: 50%\">77. The probability of winning the 2010 Megamillions lottery was about 0.0000000057. Write the number in scientific notation.<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%\">78. In 2010, the number of Facebook users each day who changed their status to \u2018engaged\u2019 was <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-f8dd1438db763c0ba7bac0a8685edc5d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#105;&#109;&#101;&#115;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#123;&#49;&#48;&#125;&#94;&#123;&#52;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"62\" style=\"vertical-align: 0px;\" \/>. Convert this number to decimal form.<\/td>\n<td style=\"width: 50%\">79. At the start of 2012, the US federal budget had a deficit of more than <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-68c8f6a058a34c07ad24f374e37719b1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#116;&#101;&#120;&#116;&#123;&#63;&#125;&#49;&#46;&#53;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#105;&#109;&#101;&#115;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#123;&#49;&#48;&#125;&#94;&#123;&#49;&#51;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"92\" style=\"vertical-align: 0px;\" \/>. Convert this number to decimal form.<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%\">80. The concentration of carbon dioxide in the atmosphere is <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-0b5f8354e80732e1a31f63ee4c49bb8b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#51;&#46;&#57;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#105;&#109;&#101;&#115;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#123;&#49;&#48;&#125;&#94;&#123;&#45;&#52;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"87\" style=\"vertical-align: 0px;\" \/>. Convert this number to decimal form.<\/td>\n<td style=\"width: 50%\">81. The width of a proton is <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-a57902d2b6ff7cee22de32c08563dc44_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#105;&#109;&#101;&#115;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#123;&#49;&#48;&#125;&#94;&#123;&#45;&#53;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"72\" style=\"vertical-align: 0px;\" \/> of the width of an atom. Convert this number to decimal form.<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%\">\n<p id=\"fs-id1169597700250\">82. <strong data-effect=\"bold\">Health care costs<\/strong> The Centers for Medicare and Medicaid projects that American consumers will spend more than &#36;4 trillion on health care by 2017<\/p>\n<ol id=\"fs-id1168746422024\" class=\"circled\" type=\"a\">\n<li>Write 4 trillion in decimal notation.<\/li>\n<li>Write 4 trillion in scientific notation.<\/li>\n<\/ol>\n<\/td>\n<td style=\"width: 50%\">83. <strong data-effect=\"bold\">Coin production<\/strong> In 1942, the U.S. Mint produced 154,500,000 nickels. Write 154,500,000 in scientific notation.<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%\">\n<p id=\"fs-id1169597704448\">84.<strong data-effect=\"bold\"> Distance<\/strong> The distance between Earth and one of the brightest stars in the night star is 33.7 light years. One light year is about 6,000,000,000,000 (6 trillion), miles.<\/p>\n<p>a) Write the number of miles in one light year in scientific notation.<\/p>\n<p>b)Use scientific notation to find the distance between Earth and the star in miles. Write the answer in scientific notation.<\/td>\n<td style=\"width: 50%\">\n<p id=\"fs-id1169597704506\">85. <strong data-effect=\"bold\">Debt<\/strong> At the end of fiscal year 2019 the gross Canadian federal government debt was estimated to be approximately &#36;685,450,000,000 (&#36;685.45 billion), according to the Federal Budget. The population of Canada was approximately 37,590,000 people at the end of fiscal year 2019<\/p>\n<p>a) Write the debt in scientific notation.<\/p>\n<p>b) Write the population in scientific notation.<\/p>\n<p>c) Find the amount of debt per person by using scientific notation to divide the debt by the population. Write the answer in scientific notation.<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<h2 style=\"text-align: left\" data-type=\"title\">Writing Exercises.<\/h2>\n<table style=\"border-collapse: collapse;width: 100%\">\n<tbody>\n<tr>\n<td style=\"width: 50%\">86.<\/p>\n<p>a) Explain the meaning of the exponent in the expression <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-cb717ac4047dc2ebff232a8f5554c3a6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#50;&#125;&#94;&#123;&#51;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"16\" style=\"vertical-align: 0px;\" \/>.<\/p>\n<p>b) Explain the meaning of the exponent in the expression <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-ebd0c4a7d3fbf67866f17a6f8e086435_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#50;&#125;&#94;&#123;&#45;&#51;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"27\" style=\"vertical-align: 0px;\" \/>.<\/td>\n<td style=\"width: 50%\">87. When you convert a number from decimal notation to scientific notation, how do you know if the exponent will be positive or negative?<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<h1>Answers<\/h1>\n<table style=\"border-collapse: collapse;width: 100%;height: 255px\">\n<tbody>\n<tr style=\"height: 17px\">\n<td style=\"width: 33.3333%;height: 17px\">1. a) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-dd81e35d9eab43ca4913357ee6a914e7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#56;&#49;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"14\" style=\"vertical-align: -6px;\" \/> b) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-8fb5cf4f8094ee73d68eeae77fd95678_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#49;&#48;&#48;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"21\" style=\"vertical-align: -6px;\" \/><\/td>\n<td style=\"width: 33.3333%;height: 17px\">3. a) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-ec216051bb2907f5ebc1bc3ba3ac0208_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#50;&#53;&#54;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"21\" style=\"vertical-align: -6px;\" \/> b) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-8fb5cf4f8094ee73d68eeae77fd95678_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#49;&#48;&#48;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"21\" style=\"vertical-align: -6px;\" \/><\/td>\n<td style=\"width: 33.3333%;height: 17px\">5. a) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-5cca95335c8e620c9fa5659cf7b29eee_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#99;&#125;&#94;&#123;&#53;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"15\" style=\"vertical-align: 0px;\" \/> b) 25<\/td>\n<\/tr>\n<tr style=\"height: 17px\">\n<td style=\"width: 33.3333%;height: 17px\">7. a) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-4f3437b0b378ae2079923b4a7d9eaf1f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#116;&#125;&#94;&#123;&#57;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"13\" style=\"vertical-align: 0px;\" \/> b) 10000<\/td>\n<td style=\"width: 33.3333%;height: 17px\">9. a) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-a2118d8521f03a531518e711a3558153_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#48;&#48;&#125;&#123;&#57;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"21\" style=\"vertical-align: -6px;\" \/> b) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-3e22a84cb4fb64c6818d44e6272eef0c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#92;&#102;&#114;&#97;&#99;&#123;&#123;&#99;&#125;&#94;&#123;&#51;&#125;&#123;&#100;&#125;&#94;&#123;&#51;&#125;&#125;&#123;&#56;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"25\" width=\"42\" style=\"vertical-align: -6px;\" \/><\/td>\n<td style=\"width: 33.3333%;height: 17px\">11. a) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-1f4d0f3099bc3c1bad42fa90d958836b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#56;&#125;&#123;&#51;&#52;&#51;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"21\" style=\"vertical-align: -6px;\" \/> b) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-a5637c9f3c346bc0e36b13d80d88dd03_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#92;&#102;&#114;&#97;&#99;&#123;&#123;&#120;&#125;&#94;&#123;&#51;&#125;&#123;&#121;&#125;&#94;&#123;&#54;&#125;&#125;&#123;&#50;&#55;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"26\" width=\"44\" style=\"vertical-align: -6px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 17px\">\n<td style=\"width: 33.3333%;height: 17px\">13. a) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-ea2d1dcf02248d8daa27c15cd901d859_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#52;&#57;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"14\" style=\"vertical-align: -6px;\" \/> b) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-2fe70375c414a59c1fb292a62854cb03_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#52;&#57;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"29\" style=\"vertical-align: -6px;\" \/>c) 49 d) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-48b5f780791c20326d1316c7be569f56_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#52;&#57;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"31\" style=\"vertical-align: 0px;\" \/><\/td>\n<td style=\"width: 33.3333%;height: 17px\">15. a) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-9e6fd86dd44e2eb5b8b830045b12fc08_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#49;&#50;&#53;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"36\" style=\"vertical-align: -6px;\" \/> b) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-caf2057e9164e12e6816a0ac4a5060a1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#49;&#50;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"39\" style=\"vertical-align: 0px;\" \/> c) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-caf2057e9164e12e6816a0ac4a5060a1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#49;&#50;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"39\" style=\"vertical-align: 0px;\" \/>d)<img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-9e6fd86dd44e2eb5b8b830045b12fc08_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#49;&#50;&#53;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"36\" style=\"vertical-align: -6px;\" \/><\/td>\n<td style=\"width: 33.3333%;height: 17px\">17. a) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-32e7c68d045135e2144262503e6537b6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#50;&#125;&#123;&#53;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"7\" style=\"vertical-align: -6px;\" \/> b) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-e300163b774c2115fe484fdb949715ce_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#49;&#48;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"14\" style=\"vertical-align: -6px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 17px\">\n<td style=\"width: 33.3333%;height: 17px\">19. a) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-d0387ce51ded0175e6f403058470743d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#51;&#125;&#123;&#49;&#54;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"14\" style=\"vertical-align: -6px;\" \/> b) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-24a0cfce4d12caafea3f63d9a2da8358_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#49;&#52;&#52;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"21\" style=\"vertical-align: -6px;\" \/><\/td>\n<td style=\"width: 33.3333%;height: 17px\">21. a)<img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-67a793aef174ad475e8f16293d674b82_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#123;&#98;&#125;&#94;&#123;&#53;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"23\" width=\"13\" style=\"vertical-align: -7px;\" \/> b) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-dc7bc63ecc8bda362df961ee395b093e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#123;&#107;&#125;&#94;&#123;&#49;&#48;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"23\" width=\"21\" style=\"vertical-align: -7px;\" \/><\/td>\n<td style=\"width: 33.3333%;height: 17px\">23. a) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-dd443a609781d90ed8aa30013aaeb802_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#123;&#115;&#125;&#94;&#123;&#56;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"23\" width=\"14\" style=\"vertical-align: -7px;\" \/> b) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-88f19dd62e497069df2afc1463f1785f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#123;&#97;&#125;&#94;&#123;&#57;&#48;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"23\" width=\"20\" style=\"vertical-align: -7px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 17px\">\n<td style=\"width: 33.3333%;height: 17px\">25. a) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-f0e8681d687d3af8a0c79bbf18c20096_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#54;&#125;&#123;&#114;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"7\" style=\"vertical-align: -6px;\" \/> b) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-5228bb6622ae7c1b93c2f610b5e4f1de_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#54;&#114;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"14\" style=\"vertical-align: -6px;\" \/>c)<img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-412105d8299de793f92765010f5066c7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#54;&#114;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"29\" style=\"vertical-align: -6px;\" \/><\/td>\n<td style=\"width: 33.3333%;height: 17px\">27. a)<img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-9bd95e7c649104bd8ca1818722b125da_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#49;&#54;&#123;&#113;&#125;&#94;&#123;&#52;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"26\" width=\"28\" style=\"vertical-align: -10px;\" \/> b) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-57d19fbe00c63b6bddb82a04c99645c7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#50;&#125;&#123;&#123;&#113;&#125;&#94;&#123;&#52;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"26\" width=\"14\" style=\"vertical-align: -10px;\" \/> c) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-ea5567bc134a09b78c72adbc76c39af2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#92;&#102;&#114;&#97;&#99;&#123;&#50;&#125;&#123;&#123;&#113;&#125;&#94;&#123;&#52;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"26\" width=\"29\" style=\"vertical-align: -10px;\" \/><\/td>\n<td style=\"width: 33.3333%;height: 17px\">29. a) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-28218cc7942aa5ae5056a9b9e5bc7126_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#123;&#115;&#125;&#94;&#123;&#52;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"23\" width=\"14\" style=\"vertical-align: -7px;\" \/> b) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-4d98e53dc15cab11e515a139368590d3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#123;&#113;&#125;&#94;&#123;&#53;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"26\" width=\"14\" style=\"vertical-align: -10px;\" \/> c) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-59c5ba9b0465281f3d4798c7af6cae0d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#123;&#121;&#125;&#94;&#123;&#55;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"26\" width=\"15\" style=\"vertical-align: -10px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 17px\">\n<td style=\"width: 33.3333%;height: 17px\">31. a) 1 b) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-2a35d6019f635d5ce7944d35227fc0c3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#121;&#125;&#94;&#123;&#54;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"16\" style=\"vertical-align: -4px;\" \/> c) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-183a8732dc80f7b96a4601a5ad9ce1f8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#123;&#121;&#125;&#94;&#123;&#52;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"26\" width=\"15\" style=\"vertical-align: -10px;\" \/><\/td>\n<td style=\"width: 33.3333%;height: 17px\">33. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-cd257d601e075d0c1e85ab0a33f88739_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#120;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"8\" style=\"vertical-align: -6px;\" \/><\/td>\n<td style=\"width: 33.3333%;height: 17px\">35. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-ab35467a8e4a3b48dbc4e776020e0d64_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#123;&#109;&#125;&#94;&#123;&#50;&#125;&#123;&#110;&#125;&#94;&#123;&#52;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"23\" width=\"35\" style=\"vertical-align: -7px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 17px\">\n<td style=\"width: 33.3333%;height: 17px\">37. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-d1cc0e3d99b6774632908b279d2238cc_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#123;&#112;&#125;&#94;&#123;&#53;&#125;&#123;&#113;&#125;&#94;&#123;&#55;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"26\" width=\"29\" style=\"vertical-align: -10px;\" \/><\/td>\n<td style=\"width: 33.3333%;height: 17px\">39. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-d159cabfc7c32168f99fb54342c04534_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#52;&#123;&#107;&#125;&#94;&#123;&#53;&#125;&#125;&#123;&#123;&#106;&#125;&#94;&#123;&#51;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"29\" width=\"44\" style=\"vertical-align: -10px;\" \/><\/td>\n<td style=\"width: 33.3333%;height: 17px\">41. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-bb38fda6c84d95760392a289e646e63e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#92;&#102;&#114;&#97;&#99;&#123;&#52;&#48;&#123;&#110;&#125;&#94;&#123;&#51;&#125;&#125;&#123;&#109;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"25\" width=\"44\" style=\"vertical-align: -6px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 17px\">\n<td style=\"width: 33.3333%;height: 17px\">43. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-3a50ac481490c23d4174378b402d1c58_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#54;&#52;&#123;&#121;&#125;&#94;&#123;&#57;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"26\" width=\"28\" style=\"vertical-align: -10px;\" \/><\/td>\n<td style=\"width: 33.3333%;height: 17px\">45. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-a82577cc23bf69d25fb9efa8068e31cd_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#52;&#125;&#123;&#123;&#112;&#125;&#94;&#123;&#49;&#48;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"26\" width=\"21\" style=\"vertical-align: -10px;\" \/><\/td>\n<td style=\"width: 33.3333%;height: 17px\">47. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-75036bb45e2b1a8de346d3e54eaf526b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#110;&#125;&#94;&#123;&#55;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"18\" style=\"vertical-align: 0px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 17px\">\n<td style=\"width: 33.3333%;height: 17px\">49. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-d626cfbe36d660eb6863fc49e2a6653e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#121;&#125;&#94;&#123;&#53;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"16\" style=\"vertical-align: -4px;\" \/><\/td>\n<td style=\"width: 33.3333%;height: 17px\">51. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-3252b630755fdba613678b46b809ed96_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#51;&#46;&#52;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#105;&#109;&#101;&#115;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#123;&#49;&#48;&#125;&#94;&#123;&#53;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"76\" style=\"vertical-align: 0px;\" \/><\/td>\n<td style=\"width: 33.3333%;height: 17px\">53. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-ed29eac74e0cb9357657e4d14d1dc937_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#46;&#50;&#57;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#105;&#109;&#101;&#115;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#123;&#49;&#48;&#125;&#94;&#123;&#54;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"84\" style=\"vertical-align: 0px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 17px\">\n<td style=\"width: 33.3333%;height: 17px\">55. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-2b2bb0e097efe6725b62a58756469c6a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#52;&#46;&#49;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#105;&#109;&#101;&#115;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#123;&#49;&#48;&#125;&#94;&#123;&#45;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"87\" style=\"vertical-align: 0px;\" \/><\/td>\n<td style=\"width: 33.3333%;height: 17px\">57. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-214331df6e5824e3a009b7e9c700aaba_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#46;&#48;&#51;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#105;&#109;&#101;&#115;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#123;&#49;&#48;&#125;&#94;&#123;&#45;&#54;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"95\" style=\"vertical-align: 0px;\" \/><\/td>\n<td style=\"width: 33.3333%;height: 17px\">59. 830<\/td>\n<\/tr>\n<tr style=\"height: 17px\">\n<td style=\"width: 33.3333%;height: 17px\">61. 16,000,000,000<\/td>\n<td style=\"width: 33.3333%;height: 17px\">63. 0.038<\/td>\n<td style=\"width: 33.3333%;height: 17px\">65. 0.0000193<\/td>\n<\/tr>\n<tr style=\"height: 17px\">\n<td style=\"width: 33.3333%;height: 17px\">67. 0.02<\/td>\n<td style=\"width: 33.3333%;height: 17px\">69. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-97c16dc1331cee0a2c51713195417a3f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#53;&#46;&#54;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#105;&#109;&#101;&#115;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#123;&#49;&#48;&#125;&#94;&#123;&#45;&#54;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"87\" style=\"vertical-align: 0px;\" \/><\/td>\n<td style=\"width: 33.3333%;height: 17px\">71. 500,000,000<\/td>\n<\/tr>\n<tr style=\"height: 17px\">\n<td style=\"width: 33.3333%;height: 17px\">73. 20,000,000<\/td>\n<td style=\"width: 33.3333%;height: 17px\">75. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-bc22b852e311a92dacbd00c32afc5d8a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#54;&#46;&#56;&#53;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#105;&#109;&#101;&#115;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#123;&#49;&#48;&#125;&#94;&#123;&#57;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"85\" style=\"vertical-align: 0px;\" \/>.<\/td>\n<td style=\"width: 33.3333%;height: 17px\">77. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-ecf8374dae38332004c5ef962ac93193_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#53;&#46;&#55;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#105;&#109;&#101;&#115;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#123;&#49;&#48;&#125;&#94;&#123;&#45;&#57;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"87\" style=\"vertical-align: 0px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 17px\">\n<td style=\"width: 33.3333%;height: 17px\">79. 15,000,000,000,000<\/td>\n<td style=\"width: 33.3333%;height: 17px\">81. 0.00001<\/td>\n<td style=\"width: 33.3333%;height: 17px\">83. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-ddf8c70e5d13ec580a64a7969115cdc4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#46;&#53;&#52;&#53;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#105;&#109;&#101;&#115;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#123;&#49;&#48;&#125;&#94;&#123;&#56;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"93\" style=\"vertical-align: 0px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 17px\">\n<td style=\"width: 33.3333%;height: 17px\" colspan=\"2\">85.<\/p>\n<ol type=\"a\">\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-eb7deec159fd67b4ad9ff54ff1550e0d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#54;&#46;&#56;&#53;&#52;&#53;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#105;&#109;&#101;&#115;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#123;&#49;&#48;&#125;&#94;&#123;&#49;&#49;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"109\" style=\"vertical-align: 0px;\" \/><\/li>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-bcab89f1d741f0de1de9c7d1daee56e7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#51;&#46;&#55;&#53;&#57;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#105;&#109;&#101;&#115;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#123;&#49;&#48;&#125;&#94;&#123;&#55;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"94\" style=\"vertical-align: 0px;\" \/><\/li>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-a080e66bf3cd353a6c22351ccdc5822e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#46;&#56;&#50;&#51;&#52;&#57;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#105;&#109;&#101;&#115;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#123;&#49;&#48;&#125;&#94;&#123;&#52;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"111\" style=\"vertical-align: 0px;\" \/><\/li>\n<\/ol>\n<\/td>\n<td style=\"width: 33.3333%;height: 17px\">87. Answers will vary<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<h1>Attributions<\/h1>\n<p>This chapter has been adapted from \u201cInteger Exponents and Scientific Notation\u201d in <a href=\"https:\/\/openstax.org\/details\/books\/elementary-algebra\"><em>Elementary Algebra<\/em> (OpenStax)<\/a> by Lynn Marecek and MaryAnne Anthony-Smith, which is under a <a href=\"https:\/\/creativecommons.org\/licenses\/by\/4.0\/\">CC BY 4.0 Licence<\/a>. Adapted by Izabela Mazur. See the Copyright page for more information.<\/p>\n","protected":false},"author":999,"menu_order":3,"template":"","meta":{"pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[48],"contributor":[],"license":[],"class_list":["post-1624","chapter","type-chapter","status-publish","hentry","chapter-type-numberless"],"part":1528,"_links":{"self":[{"href":"https:\/\/pressbooks.bccampus.ca\/math53\/wp-json\/pressbooks\/v2\/chapters\/1624","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/pressbooks.bccampus.ca\/math53\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/pressbooks.bccampus.ca\/math53\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/pressbooks.bccampus.ca\/math53\/wp-json\/wp\/v2\/users\/999"}],"version-history":[{"count":17,"href":"https:\/\/pressbooks.bccampus.ca\/math53\/wp-json\/pressbooks\/v2\/chapters\/1624\/revisions"}],"predecessor-version":[{"id":2615,"href":"https:\/\/pressbooks.bccampus.ca\/math53\/wp-json\/pressbooks\/v2\/chapters\/1624\/revisions\/2615"}],"part":[{"href":"https:\/\/pressbooks.bccampus.ca\/math53\/wp-json\/pressbooks\/v2\/parts\/1528"}],"metadata":[{"href":"https:\/\/pressbooks.bccampus.ca\/math53\/wp-json\/pressbooks\/v2\/chapters\/1624\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/pressbooks.bccampus.ca\/math53\/wp-json\/wp\/v2\/media?parent=1624"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/pressbooks.bccampus.ca\/math53\/wp-json\/pressbooks\/v2\/chapter-type?post=1624"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/pressbooks.bccampus.ca\/math53\/wp-json\/wp\/v2\/contributor?post=1624"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/pressbooks.bccampus.ca\/math53\/wp-json\/wp\/v2\/license?post=1624"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}