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

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

\(a^2⋅a^{-9}=a^{2+-9}=a^{-7}\)

\((x^9)^{-3}=x^{9⋅-3}=x^{-27}\)

\(x^3⋅{1 \over x^7}=x^3⋅x^{-7}=x^{3+-7}=x^{-4}\)

\({({1 \over a^5}) \over a^2}={a^{-5} \over a^2}=a^{-5-2}=a^{-7}\)

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

\({3 \over x^7}\)

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

\({x^5 \over ({1 \over x^7})}={x^5 \over x^{-7}}=x^{5--7}=x^{12}\)

\({5a^7b^5 \over 2a^4b^6}={5 \over 2}⋅{a^7 \over a^4}⋅{b^5 \over b^6}={5 \over 2}⋅a^{7-4}⋅a^{5-6}=2\frac{1}{2}a^3b^{-1}\)

\(a^2⋅\sqrt[5]{a}=a^2⋅a^{\frac{1}{5}}=a^{2+\frac{1}{5}}=a^{2\frac{1}{5}}\)

\(x^7⋅\sqrt[9]{x^8}=x^7⋅x^{\frac{8}{9}}=x^{7+\frac{8}{9}}=x^{7\frac{8}{9}}\)

\({x^4 \over \sqrt[9]{x^5}}={x^4 \over x^{\frac{5}{9}}}=x^{4-\frac{5}{9}}=x^{3\frac{4}{9}}\)

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

\({\sqrt[9]{a^8} \over \sqrt[7]{a^5}}={a^{\frac{8}{9}} \over a^{\frac{5}{7}}}=a^{\frac{8}{9}-\frac{5}{7}}=a^{\frac{11}{63}}\)

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

\(\sqrt{x^6}=x^{\frac{6}{2}}=x^3\)

\({a^9 \over a^7⋅\sqrt[6]{a^5}}={a^9 \over a^7⋅a^{\frac{5}{6}}}={a^9 \over a^{7\frac{5}{6}}}=a^{9-7\frac{5}{6}}=a^{1\frac{1}{6}}\)

\({2b^7 \over 3a^9}\)

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

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

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

\(\frac{3}{5}p^{-\frac{4}{9}}q^{\frac{3}{7}}=\frac{3}{5}⋅{1 \over p^{\frac{4}{9}}}⋅q^{\frac{3}{7}}={3⋅\sqrt[7]{q^3} \over 5⋅\sqrt[9]{p^4}}\)