Answer Key 9.6

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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. \(\dfrac{ab^{\frac{1}{3}}\cancel{2}b^{-\frac{5}{4}}}{\cancel{4}2a^{-\frac{1}{2}}b^{-\frac{2}{3}}} \Rightarrow \dfrac{1}{2}a^{1- -\frac{1}{2}}b^{\frac{1}{3}-\frac{5}{4}- -\frac{2}{3}} \Rightarrow \dfrac{1}{2}a^{\frac{3}{2}}b^{-\frac{1}{4}}\Rightarrow \dfrac{a^{\frac{3}{2}}}{2b^{\frac{1}{4}}}\)