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

\({5p^2 \over 8p^5}={5 \over 8}⋅{p^2 \over p^5}={5 \over 8}⋅p^{2-5}={5 \over 8}p^{-3}\)

\({a^7 \over a^{-8}}=a^{7--8}=a^{15}\)

\(a^4⋅a^{-8}=a^{4+-8}=a^{-4}\)

\((x^4)^{-3}=x^{4⋅-3}=x^{-12}\)

\(a^3⋅{1 \over a^5}=a^3⋅a^{-5}=a^{3+-5}=a^{-2}\)

\({({1 \over p^9}) \over p^7}={p^{-9} \over p^7}=p^{-9-7}=p^{-16}\)

\({x^7 \over ({1 \over x^9})}={x^7 \over x^{-9}}=x^{7--9}=x^{16}\)

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

\({x^5 \over x^0}=x^{5-0}=x^5\)

\(p^3⋅\sqrt[4]{p}=p^3⋅p^{\frac{1}{4}}=p^{3+\frac{1}{4}}=p^{3\frac{1}{4}}\)

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

\({x^5 \over \sqrt[7]{x^4}}={x^5 \over x^{\frac{4}{7}}}=x^{5-\frac{4}{7}}=x^{4\frac{3}{7}}\)

\({1 \over a^4}⋅\sqrt[7]{a^5}=a^{-4}⋅a^{\frac{5}{7}}=a^{-4+\frac{5}{7}}=a^{-3\frac{2}{7}}\)

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

\(\sqrt[9]{{1 \over p^7}}=\sqrt[9]{p^{-7}}=p^{-\frac{7}{9}}\)

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

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

\({5 \over x^6}\)

\({6b^3 \over 7a^6}\)

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

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

\(\frac{5}{7}x^{-\frac{5}{6}}y^{\frac{4}{7}}=\frac{5}{7}⋅{1 \over x^{\frac{5}{6}}}⋅y^{\frac{4}{7}}={5⋅\sqrt[7]{y^4} \over 7⋅\sqrt[6]{x^5}}\)

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