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

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

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

\(a^2⋅a^{-9}=a^{2+-9}=a^{-7}\)

\((p^9)^{-8}=p^{9⋅-8}=p^{-72}\)

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

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

\({x^5 \over ({1 \over x^6})}={x^5 \over x^{-6}}=x^{5--6}=x^{11}\)

\({3p^6q^5 \over 2p^5q^9}={3 \over 2}⋅{p^6 \over p^5}⋅{q^5 \over q^9}={3 \over 2}⋅p^{6-5}⋅p^{5-9}=1\frac{1}{2}pq^{-4}\)

\({x^0 \over x^7}=x^{0-7}=x^{-7}\)

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

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

\({p^9 \over \sqrt[7]{p^5}}={p^9 \over p^{\frac{5}{7}}}=p^{9-\frac{5}{7}}=p^{8\frac{2}{7}}\)

\({1 \over a^2}⋅\sqrt[4]{a^3}=a^{-2}⋅a^{\frac{3}{4}}=a^{-2+\frac{3}{4}}=a^{-1\frac{1}{4}}\)

\({\sqrt[8]{x^5} \over \sqrt[5]{x^2}}={x^{\frac{5}{8}} \over x^{\frac{2}{5}}}=x^{\frac{5}{8}-\frac{2}{5}}=x^{\frac{9}{40}}\)

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

\(\sqrt{a^4}=a^{\frac{4}{2}}=a^2\)

\({a^7 \over a^4⋅\sqrt[4]{a^3}}={a^7 \over a^4⋅a^{\frac{3}{4}}}={a^7 \over a^{4\frac{3}{4}}}=a^{7-4\frac{3}{4}}=a^{2\frac{1}{4}}\)

\({8 \over a^2}\)

\({3b^9 \over 7a^8}\)

\(({1 \over 4}a)^{-5}=(4^{-1}⋅a)^{-5}=(4^{-1})^{-5}⋅a^{-5}=4^5⋅a^{-5}={1\,024 \over a^5}\)

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

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

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