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

\({x^5 \over x^{-4}}=x^{5--4}=x^9\)

\(a^6⋅a^{-8}=a^{6+-8}=a^{-2}\)

\((p^6)^{-3}=p^{6⋅-3}=p^{-18}\)

\(x^7⋅{1 \over x^9}=x^7⋅x^{-9}=x^{7+-9}=x^{-2}\)

\({({1 \over p^7}) \over p^2}={p^{-7} \over p^2}=p^{-7-2}=p^{-9}\)

\({x^9 \over x^0}=x^{9-0}=x^9\)

\({3 \over a^5}\)

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

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

\({7a^4b^2 \over 5a^2b^7}={7 \over 5}⋅{a^4 \over a^2}⋅{b^2 \over b^7}={7 \over 5}⋅a^{4-2}⋅a^{2-7}=1\frac{2}{5}a^2b^{-5}\)

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

\(p^2⋅\sqrt[9]{p^7}=p^2⋅p^{\frac{7}{9}}=p^{2+\frac{7}{9}}=p^{2\frac{7}{9}}\)

\({a^2 \over \sqrt[3]{a^2}}={a^2 \over a^{\frac{2}{3}}}=a^{2-\frac{2}{3}}=a^{1\frac{1}{3}}\)

\({1 \over x^3}⋅\sqrt[7]{x^2}=x^{-3}⋅x^{\frac{2}{7}}=x^{-3+\frac{2}{7}}=x^{-2\frac{5}{7}}\)

\({\sqrt[4]{p^3} \over \sqrt[3]{p^2}}={p^{\frac{3}{4}} \over p^{\frac{2}{3}}}=p^{\frac{3}{4}-\frac{2}{3}}=p^{\frac{1}{12}}\)

\(\sqrt[8]{{1 \over a^3}}=\sqrt[8]{a^{-3}}=a^{-\frac{3}{8}}\)

\(\sqrt[4]{x^8}=x^{\frac{8}{4}}=x^2\)

\({a^4 \over a^5⋅\sqrt[9]{a^2}}={a^4 \over a^5⋅a^{\frac{2}{9}}}={a^4 \over a^{5\frac{2}{9}}}=a^{4-5\frac{2}{9}}=a^{-1\frac{2}{9}}\)

\({6b^5 \over 7a^3}\)

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

\(({1 \over 2}a)^{-4}=(2^{-1}⋅a)^{-4}=(2^{-1})^{-4}⋅a^{-4}=2^4⋅a^{-4}={16 \over a^4}\)

\(9x^{7\frac{5}{7}}=9⋅x^7⋅x^{\frac{5}{7}}=9x^7⋅\sqrt[7]{x^5}\)

\(\frac{1}{5}p^{-\frac{5}{8}}q^{\frac{4}{5}}=\frac{1}{5}⋅{1 \over p^{\frac{5}{8}}}⋅q^{\frac{4}{5}}={1⋅\sqrt[5]{q^4} \over 5⋅\sqrt[8]{p^5}}\)