Answer Key 9.6

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

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Intermediate Algebra by Terrance Berg is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License, except where otherwise noted.

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