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

\({x^5 \over x^{-9}}=x^{5--9}=x^{14}\)

\(a^4⋅a^{-8}=a^{4+-8}=a^{-4}\)

\((a^3)^{-6}=a^{3⋅-6}=a^{-18}\)

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

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

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

\({8 \over p^3}\)

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

\({a^2 \over ({1 \over a^9})}={a^2 \over a^{-9}}=a^{2--9}=a^{11}\)

\({7a^5b^5 \over 5a^4b^6}={7 \over 5}⋅{a^5 \over a^4}⋅{b^5 \over b^6}={7 \over 5}⋅a^{5-4}⋅a^{5-6}=1\frac{2}{5}ab^{-1}\)

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

\(a^2⋅\sqrt[7]{a^4}=a^2⋅a^{\frac{4}{7}}=a^{2+\frac{4}{7}}=a^{2\frac{4}{7}}\)

\({x^6 \over \sqrt[7]{x^3}}={x^6 \over x^{\frac{3}{7}}}=x^{6-\frac{3}{7}}=x^{5\frac{4}{7}}\)

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

\({\sqrt[7]{a^4} \over \sqrt[9]{a^5}}={a^{\frac{4}{7}} \over a^{\frac{5}{9}}}=a^{\frac{4}{7}-\frac{5}{9}}=a^{\frac{1}{63}}\)

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

\(\sqrt[5]{x^{20}}=x^{\frac{20}{5}}=x^4\)

\({x^3 \over x^8⋅\sqrt[9]{x^5}}={x^3 \over x^8⋅x^{\frac{5}{9}}}={x^3 \over x^{8\frac{5}{9}}}=x^{3-8\frac{5}{9}}=x^{-5\frac{5}{9}}\)

\({7b^4 \over 8a^6}\)

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

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

\(6p^{4\frac{2}{3}}=6⋅p^4⋅p^{\frac{2}{3}}=6p^4⋅\sqrt[3]{p^2}\)

\(\frac{4}{5}x^{-\frac{1}{6}}y^{\frac{8}{9}}=\frac{4}{5}⋅{1 \over x^{\frac{1}{6}}}⋅y^{\frac{8}{9}}={4⋅\sqrt[9]{y^8} \over 5⋅\sqrt[6]{x}}\)