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

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

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

\(a^4⋅a^{-7}=a^{4+-7}=a^{-3}\)

\((x^9)^{-4}=x^{9⋅-4}=x^{-36}\)

\(a^6⋅{1 \over a^9}=a^6⋅a^{-9}=a^{6+-9}=a^{-3}\)

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

\({x^3 \over ({1 \over x^5})}={x^3 \over x^{-5}}=x^{3--5}=x^8\)

\({7a^7b^3 \over 4a^4b^7}={7 \over 4}⋅{a^7 \over a^4}⋅{b^3 \over b^7}={7 \over 4}⋅a^{7-4}⋅a^{3-7}=1\frac{3}{4}a^3b^{-4}\)

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

\(x^7⋅\sqrt[4]{x}=x^7⋅x^{\frac{1}{4}}=x^{7+\frac{1}{4}}=x^{7\frac{1}{4}}\)

\(a^6⋅\sqrt[5]{a^3}=a^6⋅a^{\frac{3}{5}}=a^{6+\frac{3}{5}}=a^{6\frac{3}{5}}\)

\({x^2 \over \sqrt[7]{x^5}}={x^2 \over x^{\frac{5}{7}}}=x^{2-\frac{5}{7}}=x^{1\frac{2}{7}}\)

\({1 \over a^8}⋅\sqrt[5]{a^3}=a^{-8}⋅a^{\frac{3}{5}}=a^{-8+\frac{3}{5}}=a^{-7\frac{2}{5}}\)

\({\sqrt[5]{a^4} \over \sqrt[4]{a^3}}={a^{\frac{4}{5}} \over a^{\frac{3}{4}}}=a^{\frac{4}{5}-\frac{3}{4}}=a^{\frac{1}{20}}\)

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

\(\sqrt[4]{x^8}=x^{\frac{8}{4}}=x^2\)

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

\({8 \over a^4}\)

\({5q^3 \over 7p^2}\)

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

\(5p^{4\frac{4}{9}}=5⋅p^4⋅p^{\frac{4}{9}}=5p^4⋅\sqrt[9]{p^4}\)

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

\((3a)^{-5}=3^{-5}⋅a^{-5}={1 \over 3^5}⋅{1 \over a^5}={1 \over 243a^5}\)