\({1 \over x^3}=x^{-3}\)

\({5p^2 \over 8p^6}={5 \over 8}⋅{p^2 \over p^6}={5 \over 8}⋅p^{2-6}={5 \over 8}p^{-4}\)

\({a^9 \over a^{-8}}=a^{9--8}=a^{17}\)

\(a^3⋅a^{-6}=a^{3+-6}=a^{-3}\)

\((x^5)^{-6}=x^{5⋅-6}=x^{-30}\)

\(a^2⋅{1 \over a^8}=a^2⋅a^{-8}=a^{2+-8}=a^{-6}\)

\({({1 \over p^7}) \over p^4}={p^{-7} \over p^4}=p^{-7-4}=p^{-11}\)

\({a^7 \over ({1 \over a^8})}={a^7 \over a^{-8}}=a^{7--8}=a^{15}\)

\({9a^5b^5 \over 5a^4b^9}={9 \over 5}⋅{a^5 \over a^4}⋅{b^5 \over b^9}={9 \over 5}⋅a^{5-4}⋅a^{5-9}=1\frac{4}{5}ab^{-4}\)

\({a^0 \over a^5}=a^{0-5}=a^{-5}\)

\(p^2⋅\sqrt[6]{p}=p^2⋅p^{\frac{1}{6}}=p^{2+\frac{1}{6}}=p^{2\frac{1}{6}}\)

\(x^6⋅\sqrt[7]{x^4}=x^6⋅x^{\frac{4}{7}}=x^{6+\frac{4}{7}}=x^{6\frac{4}{7}}\)

\({x^8 \over \sqrt[7]{x^6}}={x^8 \over x^{\frac{6}{7}}}=x^{8-\frac{6}{7}}=x^{7\frac{1}{7}}\)

\({1 \over a^9}⋅\sqrt[7]{a^6}=a^{-9}⋅a^{\frac{6}{7}}=a^{-9+\frac{6}{7}}=a^{-8\frac{1}{7}}\)

\({\sqrt[7]{p^6} \over \sqrt[7]{p^3}}={p^{\frac{6}{7}} \over p^{\frac{3}{7}}}=p^{\frac{6}{7}-\frac{3}{7}}=p^{\frac{3}{7}}\)

\(\sqrt[6]{{1 \over a^5}}=\sqrt[6]{a^{-5}}=a^{-\frac{5}{6}}\)

\(\sqrt[3]{x^6}=x^{\frac{6}{3}}=x^2\)

\({a^6 \over a^2⋅\sqrt[9]{a^7}}={a^6 \over a^2⋅a^{\frac{7}{9}}}={a^6 \over a^{2\frac{7}{9}}}=a^{6-2\frac{7}{9}}=a^{3\frac{2}{9}}\)

\({2 \over x^9}\)

\({4y^4 \over 7x^3}\)

\(({1 \over 3}x)^{-2}=(3^{-1}⋅x)^{-2}=(3^{-1})^{-2}⋅x^{-2}=3^2⋅x^{-2}={9 \over x^2}\)

\(4p^{7\frac{4}{5}}=4⋅p^7⋅p^{\frac{4}{5}}=4p^7⋅\sqrt[5]{p^4}\)

\(\frac{8}{9}x^{-\frac{2}{9}}y^{\frac{7}{8}}=\frac{8}{9}⋅{1 \over x^{\frac{2}{9}}}⋅y^{\frac{7}{8}}={8⋅\sqrt[8]{y^7} \over 9⋅\sqrt[9]{x^2}}\)

\((4p)^{-3}=4^{-3}⋅p^{-3}={1 \over 4^3}⋅{1 \over p^3}={1 \over 64p^3}\)