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

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

\(x^2⋅x^{-5}=x^{2+-5}=x^{-3}\)

\((x^9)^{-4}=x^{9⋅-4}=x^{-36}\)

\(p^2⋅{1 \over p^8}=p^2⋅p^{-8}=p^{2+-8}=p^{-6}\)

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

\({a^0 \over a^2}=a^{0-2}=a^{-2}\)

\({3 \over x^2}\)

\({4a^2 \over 5a^5}={4 \over 5}⋅{a^2 \over a^5}={4 \over 5}⋅a^{2-5}={4 \over 5}a^{-3}\)

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

\({9a^5b^2 \over 8a^4b^3}={9 \over 8}⋅{a^5 \over a^4}⋅{b^2 \over b^3}={9 \over 8}⋅a^{5-4}⋅a^{2-3}=1\frac{1}{8}ab^{-1}\)

\(x^5⋅\sqrt[3]{x}=x^5⋅x^{\frac{1}{3}}=x^{5+\frac{1}{3}}=x^{5\frac{1}{3}}\)

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

\({a^7 \over \sqrt[3]{a^2}}={a^7 \over a^{\frac{2}{3}}}=a^{7-\frac{2}{3}}=a^{6\frac{1}{3}}\)

\({1 \over p^6}⋅\sqrt[9]{p^7}=p^{-6}⋅p^{\frac{7}{9}}=p^{-6+\frac{7}{9}}=p^{-5\frac{2}{9}}\)

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

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

\(\sqrt{a^8}=a^{\frac{8}{2}}=a^4\)

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

\({2b^7 \over 5a^9}\)

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

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

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

\(\frac{5}{6}x^{-\frac{3}{4}}y^{\frac{3}{8}}=\frac{5}{6}⋅{1 \over x^{\frac{3}{4}}}⋅y^{\frac{3}{8}}={5⋅\sqrt[8]{y^3} \over 6⋅\sqrt[4]{x^3}}\)