Answer Key 9.7

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

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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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