Answer Key 9.7

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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