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

\({x^7 \over x^{-5}}=x^{7--5}=x^{12}\)

\(x^3⋅x^{-9}=x^{3+-9}=x^{-6}\)

\((p^7)^{-8}=p^{7⋅-8}=p^{-56}\)

\(a^3⋅{1 \over a^6}=a^3⋅a^{-6}=a^{3+-6}=a^{-3}\)

\({({1 \over x^8}) \over x^5}={x^{-8} \over x^5}=x^{-8-5}=x^{-13}\)

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

\({5 \over a^4}\)

\({2p^4 \over 3p^8}={2 \over 3}⋅{p^4 \over p^8}={2 \over 3}⋅p^{4-8}={2 \over 3}p^{-4}\)

\({x^3 \over ({1 \over x^9})}={x^3 \over x^{-9}}=x^{3--9}=x^{12}\)

\({7x^6y^5 \over 2x^4y^9}={7 \over 2}⋅{x^6 \over x^4}⋅{y^5 \over y^9}={7 \over 2}⋅x^{6-4}⋅x^{5-9}=3\frac{1}{2}x^2y^{-4}\)

\(p^2⋅\sqrt[5]{p}=p^2⋅p^{\frac{1}{5}}=p^{2+\frac{1}{5}}=p^{2\frac{1}{5}}\)

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

\({a^6 \over \sqrt[9]{a^5}}={a^6 \over a^{\frac{5}{9}}}=a^{6-\frac{5}{9}}=a^{5\frac{4}{9}}\)

\({1 \over a^6}⋅\sqrt[5]{a^4}=a^{-6}⋅a^{\frac{4}{5}}=a^{-6+\frac{4}{5}}=a^{-5\frac{1}{5}}\)

\({\sqrt[7]{p^4} \over \sqrt[9]{p^4}}={p^{\frac{4}{7}} \over p^{\frac{4}{9}}}=p^{\frac{4}{7}-\frac{4}{9}}=p^{\frac{8}{63}}\)

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

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

\({x^6 \over x^3⋅\sqrt[5]{x^3}}={x^6 \over x^3⋅x^{\frac{3}{5}}}={x^6 \over x^{3\frac{3}{5}}}=x^{6-3\frac{3}{5}}=x^{2\frac{2}{5}}\)

\({2b^2 \over 9a^6}\)

\((3a)^{-4}=3^{-4}⋅a^{-4}={1 \over 3^4}⋅{1 \over a^4}={1 \over 81a^4}\)

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

\(2a^{8\frac{3}{7}}=2⋅a^8⋅a^{\frac{3}{7}}=2a^8⋅\sqrt[7]{a^3}\)

\(\frac{2}{5}a^{-\frac{1}{2}}b^{\frac{1}{8}}=\frac{2}{5}⋅{1 \over a^{\frac{1}{2}}}⋅b^{\frac{1}{8}}={2⋅\sqrt[8]{b} \over 5⋅\sqrt{a}}\)