\({1 \over p^5}=p^{-5}\)

\({x^3 \over x^{-6}}=x^{3--6}=x^9\)

\(a^2⋅a^{-6}=a^{2+-6}=a^{-4}\)

\((x^8)^{-4}=x^{8⋅-4}=x^{-32}\)

\(a^8⋅{1 \over a^9}=a^8⋅a^{-9}=a^{8+-9}=a^{-1}\)

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

\({a^0 \over a^4}=a^{0-4}=a^{-4}\)

\({7 \over x^8}\)

\({6a^3 \over 7a^4}={6 \over 7}⋅{a^3 \over a^4}={6 \over 7}⋅a^{3-4}={6 \over 7}a^{-1}\)

\({x^2 \over ({1 \over x^8})}={x^2 \over x^{-8}}=x^{2--8}=x^{10}\)

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

\(a^4⋅\sqrt[6]{a}=a^4⋅a^{\frac{1}{6}}=a^{4+\frac{1}{6}}=a^{4\frac{1}{6}}\)

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

\({x^6 \over \sqrt[5]{x^2}}={x^6 \over x^{\frac{2}{5}}}=x^{6-\frac{2}{5}}=x^{5\frac{3}{5}}\)

\({1 \over x^5}⋅\sqrt[8]{x^5}=x^{-5}⋅x^{\frac{5}{8}}=x^{-5+\frac{5}{8}}=x^{-4\frac{3}{8}}\)

\({\sqrt[9]{a^8} \over \sqrt[3]{a^2}}={a^{\frac{8}{9}} \over a^{\frac{2}{3}}}=a^{\frac{8}{9}-\frac{2}{3}}=a^{\frac{2}{9}}\)

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

\(\sqrt[4]{x^{16}}=x^{\frac{16}{4}}=x^4\)

\({p^9 \over p^7⋅\sqrt[9]{p^5}}={p^9 \over p^7⋅p^{\frac{5}{9}}}={p^9 \over p^{7\frac{5}{9}}}=p^{9-7\frac{5}{9}}=p^{1\frac{4}{9}}\)

\({4y^2 \over 9x^3}\)

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

\(({1 \over 5}a)^{-4}=(5^{-1}⋅a)^{-4}=(5^{-1})^{-4}⋅a^{-4}=5^4⋅a^{-4}={625 \over a^4}\)

\(8a^{5\frac{8}{9}}=8⋅a^5⋅a^{\frac{8}{9}}=8a^5⋅\sqrt[9]{a^8}\)

\(\frac{1}{3}p^{-\frac{4}{5}}q^{\frac{2}{3}}=\frac{1}{3}⋅{1 \over p^{\frac{4}{5}}}⋅q^{\frac{2}{3}}={1⋅\sqrt[3]{q^2} \over 3⋅\sqrt[5]{p^4}}\)