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

\({5x^4 \over 8x^9}={5 \over 8}⋅{x^4 \over x^9}={5 \over 8}⋅x^{4-9}={5 \over 8}x^{-5}\)

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

\(a^5⋅a^{-7}=a^{5+-7}=a^{-2}\)

\((x^5)^{-3}=x^{5⋅-3}=x^{-15}\)

\(x^8⋅{1 \over x^9}=x^8⋅x^{-9}=x^{8+-9}=x^{-1}\)

\({a^9 \over a^0}=a^{9-0}=a^9\)

\({4 \over p^2}\)

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

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

\(a^5⋅\sqrt[7]{a^2}=a^5⋅a^{\frac{2}{7}}=a^{5+\frac{2}{7}}=a^{5\frac{2}{7}}\)

\({x^2 \over \sqrt[7]{x^4}}={x^2 \over x^{\frac{4}{7}}}=x^{2-\frac{4}{7}}=x^{1\frac{3}{7}}\)

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

\({\sqrt[6]{a^5} \over \sqrt[4]{a^3}}={a^{\frac{5}{6}} \over a^{\frac{3}{4}}}=a^{\frac{5}{6}-\frac{3}{4}}=a^{\frac{1}{12}}\)

\(\sqrt[5]{x^{15}}=x^{\frac{15}{5}}=x^3\)

\({x^7 \over x^8⋅\sqrt[7]{x^5}}={x^7 \over x^8⋅x^{\frac{5}{7}}}={x^7 \over x^{8\frac{5}{7}}}=x^{7-8\frac{5}{7}}=x^{-1\frac{5}{7}}\)

\(5p^{8\frac{8}{9}}=5⋅p^8⋅p^{\frac{8}{9}}=5p^8⋅\sqrt[9]{p^8}\)