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

\({x^3 \over x^{-2}}=x^{3--2}=x^5\)

\(x^4⋅x^{-6}=x^{4+-6}=x^{-2}\)

\((a^2)^{-5}=a^{2⋅-5}=a^{-10}\)

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

\({({1 \over x^5}) \over x^4}={x^{-5} \over x^4}=x^{-5-4}=x^{-9}\)

\({p^6 \over p^0}=p^{6-0}=p^6\)

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

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

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

\({9a^2b^4 \over 8ab^6}={9 \over 8}⋅{a^2 \over a^1}⋅{b^4 \over b^6}={9 \over 8}⋅a^{2-1}⋅a^{4-6}=1\frac{1}{8}ab^{-2}\)

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

\(x^8⋅\sqrt[5]{x^3}=x^8⋅x^{\frac{3}{5}}=x^{8+\frac{3}{5}}=x^{8\frac{3}{5}}\)

\({x^9 \over \sqrt[3]{x^2}}={x^9 \over x^{\frac{2}{3}}}=x^{9-\frac{2}{3}}=x^{8\frac{1}{3}}\)

\({1 \over p^6}⋅\sqrt[9]{p^8}=p^{-6}⋅p^{\frac{8}{9}}=p^{-6+\frac{8}{9}}=p^{-5\frac{1}{9}}\)

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

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

\(\sqrt[3]{p^{12}}=p^{\frac{12}{3}}=p^4\)

\({x^2 \over x^6⋅\sqrt[9]{x^8}}={x^2 \over x^6⋅x^{\frac{8}{9}}}={x^2 \over x^{6\frac{8}{9}}}=x^{2-6\frac{8}{9}}=x^{-4\frac{8}{9}}\)

\({4y^7 \over 9x^4}\)

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

\(({1 \over 4}x)^{-3}=(4^{-1}⋅x)^{-3}=(4^{-1})^{-3}⋅x^{-3}=4^3⋅x^{-3}={64 \over x^3}\)

\(6a^{7\frac{7}{8}}=6⋅a^7⋅a^{\frac{7}{8}}=6a^7⋅\sqrt[8]{a^7}\)

\(\frac{1}{8}x^{-\frac{4}{5}}y^{\frac{4}{9}}=\frac{1}{8}⋅{1 \over x^{\frac{4}{5}}}⋅y^{\frac{4}{9}}={1⋅\sqrt[9]{y^4} \over 8⋅\sqrt[5]{x^4}}\)