Answer Key 9.6

  1. \sqrt[5]{m^3}
  2. \dfrac{1}{\sqrt[4]{(10r)^3}}
  3. \sqrt{(7x)^3}
  4. \dfrac{1}{\sqrt[3]{(6b)^4}}
  5. \dfrac{1}{\sqrt{(2x+3)^3}}
  6. \sqrt[4]{(x-3y)^3}
  7. 5^{\frac{1}{3}}
  8. 2^{\frac{3}{5}}
  9. (ab^5)^{\frac{1}{3}} or a^{\frac{1}{3}}b^{\frac{5}{3}}
  10. x^{\frac{3}{5}}
  11. (a+5)^{\frac{2}{3}}
  12. (a-2)^{\frac{3}{5}}
  13. 8^{\frac{2}{3}}\Rightarrow (2^3)^{\frac{2}{3}}\Rightarrow 2^2\text{ or }4
  14. 16^{\frac{1}{4}}\Rightarrow (2^4)^{\frac{1}{4}}\Rightarrow 2
  15. \sqrt[3]{4^6}\Rightarrow (2^2)^{\frac{6}{3}}\Rightarrow 2^4\text{ or }16
  16. \sqrt[5]{32^2}\Rightarrow (2^5)^{\frac{2}{5}}\Rightarrow 2^2\text{ or }4
  17. x^2y^{\frac{1}{3}+\frac{2}{3}}\Rightarrow x^2y
  18. 4v^{\frac{2}{3}-1}\Rightarrow 4v^{-\frac{1}{3}}\text{ or }\dfrac{4}{v^{\frac{1}{3}}}
  19. a^{-\frac{1}{2}}b^{-\frac{1}{2}}\Rightarrow \dfrac{1}{a^{\frac{1}{2}}b^{\frac{1}{2}}}}
  20. 1
  21. \dfrac{\cancel{a^2}\cancel{b^0}1}{3\cancel{a^4}a^2}\Rightarrow \dfrac{1}{3a^2}
  22. \dfrac{\cancel{2}x^{\frac{1}{2}}y^{\frac{1}{3}}}{\cancel{2}x^{\frac{4}{3}}y^{\frac{7}{4}}} \Rightarrow x^{\frac{1}{2}-\frac{4}{3}}y^{\frac{1}{3}-\frac{7}{4}}\Rightarrow x^{-\frac{5}{6}}y^{-\frac{17}{12}}\Rightarrow \dfrac{1}{x^{\frac{5}{6}}y^{\frac{17}{12}}}
  23. \dfrac{a^{\frac{3}{4}}\cancel{b^{-1}}b^{\frac{7}{4}}}{3\cancel{b^{-1}}}\Rightarrow \dfrac{a^{\frac{3}{4}}b^{\frac{7}{4}}}{3}
  24. 2x^{-2+\frac{5}{4}-1}y^{\frac{5}{3}+\frac{5}{3}-\frac{1}{2}} \Rightarrow 2x^{-\frac{7}{4}}y^{\frac{17}{6}}\Rightarrow \dfrac{2y^{\frac{17}{6}}}{x^{\frac{7}{4}}}
  25. \dfrac{3}{2}y^{-\frac{5}{4}- -1 - -\frac{1}{3}} \Rightarrow \dfrac{3}{2}y^{\frac{1}{12}}
  26. \dfrac{ab^{\frac{1}{3}}\cancel{2}b^{-\frac{5}{4}}}{\cancel{4}2a^{-\frac{1}{2}}b^{-\frac{2}{3}}} \Rightarrow \dfrac{1}{2}a^{1- -\frac{1}{2}}b^{\frac{1}{3}-\frac{5}{4}- -\frac{2}{3}} \Rightarrow \dfrac{1}{2}a^{\frac{3}{2}}b^{-\frac{1}{4}}\Rightarrow \dfrac{a^{\frac{3}{2}}}{2b^{\frac{1}{4}}}

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