\({1 \over x^4}=x^{-4}\)

\({2a \over 5a^6}={2 \over 5}⋅{a \over a^6}={2 \over 5}⋅a^{1-6}={2 \over 5}a^{-5}\)

\({p^3 \over p^{-9}}=p^{3--9}=p^{12}\)

\(x^3⋅x^{-8}=x^{3+-8}=x^{-5}\)

\((a^9)^{-8}=a^{9⋅-8}=a^{-72}\)

\(x^2⋅{1 \over x^6}=x^2⋅x^{-6}=x^{2+-6}=x^{-4}\)

\({({1 \over x^7}) \over x^6}={x^{-7} \over x^6}=x^{-7-6}=x^{-13}\)

\({a^2 \over ({1 \over a^9})}={a^2 \over a^{-9}}=a^{2--9}=a^{11}\)

\({9p^8q^5 \over 7p^3q^9}={9 \over 7}⋅{p^8 \over p^3}⋅{q^5 \over q^9}={9 \over 7}⋅p^{8-3}⋅p^{5-9}=1\frac{2}{7}p^5q^{-4}\)

\({a^0 \over a^3}=a^{0-3}=a^{-3}\)

\(x^7⋅\sqrt[3]{x}=x^7⋅x^{\frac{1}{3}}=x^{7+\frac{1}{3}}=x^{7\frac{1}{3}}\)

\(a^6⋅\sqrt[3]{a^2}=a^6⋅a^{\frac{2}{3}}=a^{6+\frac{2}{3}}=a^{6\frac{2}{3}}\)

\({x^8 \over \sqrt[9]{x^5}}={x^8 \over x^{\frac{5}{9}}}=x^{8-\frac{5}{9}}=x^{7\frac{4}{9}}\)

\({1 \over p^7}⋅\sqrt[6]{p^5}=p^{-7}⋅p^{\frac{5}{6}}=p^{-7+\frac{5}{6}}=p^{-6\frac{1}{6}}\)

\({\sqrt[4]{a^3} \over \sqrt[7]{a^3}}={a^{\frac{3}{4}} \over a^{\frac{3}{7}}}=a^{\frac{3}{4}-\frac{3}{7}}=a^{\frac{9}{28}}\)

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

\(\sqrt{x^{10}}=x^{\frac{10}{2}}=x^5\)

\({x^7 \over x^8⋅\sqrt[7]{x^4}}={x^7 \over x^8⋅x^{\frac{4}{7}}}={x^7 \over x^{8\frac{4}{7}}}=x^{7-8\frac{4}{7}}=x^{-1\frac{4}{7}}\)

\({6 \over a^2}\)

\({5q^8 \over 8p^2}\)

\(({1 \over 2}x)^{-5}=(2^{-1}⋅x)^{-5}=(2^{-1})^{-5}⋅x^{-5}=2^5⋅x^{-5}={32 \over x^5}\)

\(9a^{4\frac{2}{5}}=9⋅a^4⋅a^{\frac{2}{5}}=9a^4⋅\sqrt[5]{a^2}\)

\(\frac{4}{5}x^{-\frac{1}{3}}y^{\frac{1}{7}}=\frac{4}{5}⋅{1 \over x^{\frac{1}{3}}}⋅y^{\frac{1}{7}}={4⋅\sqrt[7]{y} \over 5⋅\sqrt[3]{x}}\)

\((2p)^{-3}=2^{-3}⋅p^{-3}={1 \over 2^3}⋅{1 \over p^3}={1 \over 8p^3}\)