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

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

\(x^6⋅x^{-7}=x^{6+-7}=x^{-1}\)

\((a^9)^{-8}=a^{9⋅-8}=a^{-72}\)

\(p^4⋅{1 \over p^9}=p^4⋅p^{-9}=p^{4+-9}=p^{-5}\)

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

\({p^0 \over p^3}=p^{0-3}=p^{-3}\)

\({6 \over x^7}\)

\({5a^3 \over 8a^4}={5 \over 8}⋅{a^3 \over a^4}={5 \over 8}⋅a^{3-4}={5 \over 8}a^{-1}\)

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

\({7p^{10}q^2 \over 3p^5q^6}={7 \over 3}⋅{p^{10} \over p^5}⋅{q^2 \over q^6}={7 \over 3}⋅p^{10-5}⋅p^{2-6}=2\frac{1}{3}p^5q^{-4}\)

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

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

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

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

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

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

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

\({a^7 \over a^2⋅\sqrt[5]{a^3}}={a^7 \over a^2⋅a^{\frac{3}{5}}}={a^7 \over a^{2\frac{3}{5}}}=a^{7-2\frac{3}{5}}=a^{4\frac{2}{5}}\)

\({5y^6 \over 6x^4}\)

\((2x)^{-3}=2^{-3}⋅x^{-3}={1 \over 2^3}⋅{1 \over x^3}={1 \over 8x^3}\)

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

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

\(\frac{1}{5}x^{-\frac{1}{6}}y^{\frac{5}{9}}=\frac{1}{5}⋅{1 \over x^{\frac{1}{6}}}⋅y^{\frac{5}{9}}={1⋅\sqrt[9]{y^5} \over 5⋅\sqrt[6]{x}}\)