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

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

\(x^2⋅x^{-3}=x^{2+-3}=x^{-1}\)

\((a^2)^{-5}=a^{2⋅-5}=a^{-10}\)

\(x^3⋅{1 \over x^7}=x^3⋅x^{-7}=x^{3+-7}=x^{-4}\)

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

\({a^0 \over a^8}=a^{0-8}=a^{-8}\)

\({5 \over a^8}\)

\({3a^2 \over 5a^7}={3 \over 5}⋅{a^2 \over a^7}={3 \over 5}⋅a^{2-7}={3 \over 5}a^{-5}\)

\({a^3 \over ({1 \over a^8})}={a^3 \over a^{-8}}=a^{3--8}=a^{11}\)

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

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

\(a^9⋅\sqrt[7]{a^4}=a^9⋅a^{\frac{4}{7}}=a^{9+\frac{4}{7}}=a^{9\frac{4}{7}}\)

\({x^4 \over \sqrt[7]{x^6}}={x^4 \over x^{\frac{6}{7}}}=x^{4-\frac{6}{7}}=x^{3\frac{1}{7}}\)

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

\({\sqrt[7]{x^4} \over \sqrt[8]{x^3}}={x^{\frac{4}{7}} \over x^{\frac{3}{8}}}=x^{\frac{4}{7}-\frac{3}{8}}=x^{\frac{11}{56}}\)

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

\(\sqrt[4]{p^{20}}=p^{\frac{20}{4}}=p^5\)

\({a^2 \over a^8⋅\sqrt[5]{a^4}}={a^2 \over a^8⋅a^{\frac{4}{5}}}={a^2 \over a^{8\frac{4}{5}}}=a^{2-8\frac{4}{5}}=a^{-6\frac{4}{5}}\)

\({2q^8 \over 3p^2}\)

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

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

\(9x^{2\frac{3}{5}}=9⋅x^2⋅x^{\frac{3}{5}}=9x^2⋅\sqrt[5]{x^3}\)

\(\frac{8}{9}x^{-\frac{4}{9}}y^{\frac{4}{7}}=\frac{8}{9}⋅{1 \over x^{\frac{4}{9}}}⋅y^{\frac{4}{7}}={8⋅\sqrt[7]{y^4} \over 9⋅\sqrt[9]{x^4}}\)