5.6 Chapter Review
Review Exercises
Simplify Expressions with Exponents
In the following exercises, simplify.
1. | 2. |
3. | 4. |
5. | 6. |
Simplify Expressions Using the Product Property for Exponents
In the following exercises, simplify each expression.
7. | 8. |
9. | 10. |
11. | 12. |
Simplify Expressions Using the Power Property for Exponents
In the following exercises, simplify each expression.
13. | 14. |
15. | 16. |
Simplify Expressions Using the Product to a Power Property
In the following exercises, simplify each expression.
17. | 18 |
19. | 20. |
Simplify Expressions by Applying Several Properties
In the following exercises, simplify each expression.
21. | 22. |
23. | 24. |
25. | 26. |
Simplify Expressions Using the Quotient Property for Exponents
In the following exercises, simplify.
27. | 28. |
29. | 30. |
31. | 32. |
Simplify Expressions with Zero Exponents
In the following exercises, simplify.
33. | 34. |
35. | 36. |
37. | 38. |
39. | 40. |
Simplify Expressions Using the Quotient to a Power Property
In the following exercises, simplify.
41. | 42. |
43. | 44. |
Simplify Expressions by Applying Several Properties
In the following exercises, simplify.
45. | 46. |
47. | 48. |
49. | 50. |
51. | 52. |
Divide Monomials
In the following exercises, divide the monomials.
53. | 54. ÷ |
55. | 56. |
Use the Definition of a Negative Exponent
In the following exercises, simplify.
57. | 58. |
59. | 60. |
61. | 62. |
Simplify Expressions with Integer Exponents
In the following exercises, simplify.
63. | 64. |
65. | 66. |
67. | 68. |
69. | 70. |
Convert from Decimal Notation to Scientific Notation
In the following exercises, write each number in scientific notation.
71. 0.00429 | 72. 8,500,000 |
73. In 2015, the population of the world was about 7,200,000,000 people. | 74. The thickness of a dime is about 0.053 inches. |
Convert Scientific Notation to Decimal Form
In the following exercises, convert each number to decimal form.
75. 1.5 × | 76. 3.8 × |
77. 5.5 × | 78. 9.1 × |
Multiply and Divide Using Scientific Notation
In the following exercises, multiply and write your answer in decimal form.
79. (3.5 ×(6.2 × | 80. (2 × (4 × |
In the following exercises, divide and write your answer in decimal form.
81. | 82. |
Simplify Expressions with Square Roots
In the following exercises, simplify.
83.
85. 87. 89. |
84.
86. 88. 90. |
Estimate Square Roots
In the following exercises, estimate each square root between two consecutive whole numbers.
91. | 92. |
Approximate Square Roots
In the following exercises, approximate each square root and round to two decimal places.
93. | 94. |
Simplify Variable Expressions with Square Roots
In the following exercises, simplify. (Assume all variables are greater than or equal to zero.)
95.
97. 99. 101. |
96.
98. 100. 102. |
Use Square Roots in Applications
In the following exercises, solve. Round to one decimal place.
Formulas:
|
103.Landscaping Janet wants to plant a square flower garden in her yard. She has enough topsoil to cover an area of square feet. How long can a side of the flower garden be?
105. Accident investigation The skid marks of a car involved in an accident were feet. How fast had the car been going before applying the brakes? |
104. Art Diego has square inch tiles. He wants to use them to make a square mosaic. How long can each side of the mosaic be?
106. Gravity A hiker dropped a granola bar from a lookout spot feet above a valley. How long did it take the granola bar to reach the valley floor? |
Review Exercise Answers
1. 17 | 3. 0.125 |
5. | 7. |
9. | 11. |
13. | 15. |
17. | 19. |
21. | 23. |
25. | 27. |
29. | 31. |
33. 1 | 35. 1 |
37. 1 | 39. 0 |
41. | 43. |
45. 1 | 47. |
49. | 51. |
53. | 55. |
57. | 59. |
61. | 63. |
65. | 67. |
69. | 71. |
73. | 75. |
77. | 79. |
81. | 83. 12 |
85. −9 | 87. not a real number |
89. 17 | 91. |
93. 7.55 | 95. 8b |
97. 15mn | 99. 7y |
101. 11cd | 103. 5.5 feet |
105. 72 mph |
Practice Test
In the following exercises, simplify each expression.
1. | 2. |
3. | 4. |
5. | 6. |
7. | 8. |
9. | 10. |
11. | 12. |
13. | 14. |
15. | 16. |
17. | 18. |
19. | 20. |
21. Convert 83,000,000 to scientific notation. | 22. Convert to decimal form. |
1. | 2. |
3. | 4. |
5. | 6. |
7. | 8. |
9. | 10. |
11. | 12. |
13. | 14. |
15. 9 | 16. -7 |
17. not a real number | 18. |
19. | 20. |
21. | 22. 0.0000691 |