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

\({6x^2 \over 7x^3}={6 \over 7}⋅{x^2 \over x^3}={6 \over 7}⋅x^{2-3}={6 \over 7}x^{-1}\)

\({a^4 \over a^{-9}}=a^{4--9}=a^{13}\)

\(p^3⋅p^{-5}=p^{3+-5}=p^{-2}\)

\((a^8)^{-5}=a^{8⋅-5}=a^{-40}\)

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

\({({1 \over p^9}) \over p^4}={p^{-9} \over p^4}=p^{-9-4}=p^{-13}\)

\({x^6 \over ({1 \over x^9})}={x^6 \over x^{-9}}=x^{6--9}=x^{15}\)

\({5p^{10}q \over 2p^5q^5}={5 \over 2}⋅{p^{10} \over p^5}⋅{q^1 \over q^5}={5 \over 2}⋅p^{10-5}⋅p^{1-5}=2\frac{1}{2}p^5q^{-4}\)

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

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

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

\({a^9 \over \sqrt[4]{a^3}}={a^9 \over a^{\frac{3}{4}}}=a^{9-\frac{3}{4}}=a^{8\frac{1}{4}}\)

\({1 \over x^3}⋅\sqrt[9]{x^4}=x^{-3}⋅x^{\frac{4}{9}}=x^{-3+\frac{4}{9}}=x^{-2\frac{5}{9}}\)

\({\sqrt[6]{p^5} \over \sqrt[8]{p^3}}={p^{\frac{5}{6}} \over p^{\frac{3}{8}}}=p^{\frac{5}{6}-\frac{3}{8}}=p^{\frac{11}{24}}\)

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

\(\sqrt[3]{x^9}=x^{\frac{9}{3}}=x^3\)

\({x^2 \over x^6⋅\sqrt[9]{x^4}}={x^2 \over x^6⋅x^{\frac{4}{9}}}={x^2 \over x^{6\frac{4}{9}}}=x^{2-6\frac{4}{9}}=x^{-4\frac{4}{9}}\)

\({7 \over a^5}\)

\({4y^4 \over 9x^5}\)

\(({1 \over 5}a)^{-2}=(5^{-1}⋅a)^{-2}=(5^{-1})^{-2}⋅a^{-2}=5^2⋅a^{-2}={25 \over a^2}\)

\(2a^{3\frac{3}{5}}=2⋅a^3⋅a^{\frac{3}{5}}=2a^3⋅\sqrt[5]{a^3}\)

\(\frac{1}{9}x^{-\frac{3}{5}}y^{\frac{1}{5}}=\frac{1}{9}⋅{1 \over x^{\frac{3}{5}}}⋅y^{\frac{1}{5}}={1⋅\sqrt[5]{y} \over 9⋅\sqrt[5]{x^3}}\)

\((5a)^{-2}=5^{-2}⋅a^{-2}={1 \over 5^2}⋅{1 \over a^2}={1 \over 25a^2}\)