Answer Key 9.7

  1. [latex](x^{-2--2}y^{-6-4})^2[/latex]
    [latex](1\cancel{x^0}y^{-10})^2[/latex]
    [latex]y^{-20}\text{ or }\dfrac{1}{y^{20}}[/latex]
  2. [latex](x^{-3--1}y^{-3-6})^3[/latex]
    [latex](x^{-2}y^{-9})^3[/latex]
    [latex]x^{-6}y^{-27}\text{ or }\dfrac{1}{x^6y^{27}}[/latex]
  3. [latex](x^{-2-2}y^{-4--4})^2[/latex]
    [latex](x^{-4}\cancel{y^0}1)^2[/latex]
    [latex]x^{-8}\text{ or }\dfrac{1}{x^8}[/latex]
  4. [latex](x^{-5--4}y^{-3-2})^4[/latex]
    [latex](x^{-1}y^{-5})^4[/latex]
    [latex]x^{-4}y^{-20}\text{ or }\dfrac{1}{x^4y^{20}}[/latex]
  5. [latex](x^{-2--3}y^{-2-3})^8[/latex]
    [latex](x^1y^{-5})^8[/latex]
    [latex]x^8y^{-40}\text{ or }\dfrac{x^8}{y^{40}}[/latex]
  6. [latex](x^{-4--3}y^{-3-2})^5[/latex]
    [latex](x^{-1}y^{-5})^5[/latex]
    [latex]x^{-5}y^{-25}\text{ or }\dfrac{1}{x^5y^{25}}[/latex]
  7. [latex](x^{-2--2}y^{-4-4})^{-2}[/latex]
    [latex](1\cancel{x^0}y^{-8})^{-2}[/latex]
    [latex]y^{16}[/latex]
  8. [latex](x^{-2--5}y^{-3-3})^{-3}[/latex]
    [latex](x^3y^{-6})^{-3}[/latex]
    [latex]x^{-9}y^{18}\text{ or }\dfrac{y^{18}}{x^9}[/latex]
  9. [latex](x^{-2--2}y^{-3--3})^{-1}[/latex]
    [latex](\cancel{x^0y^0}1)^{-1}[/latex]
    1
  10. [latex](x^{-2--2}y^{-3--4}})^{-2}[/latex]
    [latex](x^0y^{-7})^{-2}[/latex]
    [latex]y^{14}[/latex]
  11. [latex]\left(\dfrac{1\cancel{x^0}y^{-3}}{x^{-2}\cancel{y^0}1}\right)^{-5} \\[/latex]
    [latex]\left(\dfrac{x^2}{y^3}\right)^{-5} \\[/latex]
    [latex]\dfrac{x^{-10}}{y^{-15}} \\[/latex]
    [latex]\dfrac{y^{15}}{x^{10}}[/latex]
  12. 1
  13. [latex]\left(\dfrac{1 \cancel{a^0}b^3}{a^6b^{-12}}\right)^{-\frac{1}{3}} \\[/latex]
    [latex]\left(\dfrac{b^{15}}{a^6}\right)^{-\frac{1}{3}} \\[/latex]
    [latex]\dfrac{b^{-5}}{a^{-2}}\text{ or }\dfrac{a^2}{b^5}[/latex]
  14. [latex](a^4b^4c^{12})^{\frac{1}{4}}[/latex]
    [latex]abc^3[/latex]
  15. [latex]\left(\dfrac{a^5c^{10}d^{15}}{b^5}\right)^{\frac{2}{5}} \\[/latex]
    [latex]\dfrac{a^2c^4d^6}{b^2}[/latex]
  16. [latex]\left(\dfrac{b^{20}}{a^4}\right)^{-\frac{3}{4}} \\[/latex]
    [latex]\dfrac{b^{-15}}{a^{-3}}\text{ or }\dfrac{a^3}{b^{15}}[/latex]
  17. 1
  18. Undefined

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Intermediate Algebra (Convert to MathJax) Copyright © 2020 by Terrance Berg is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License, except where otherwise noted.

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