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

\({p^7 \over p^{-3}}=p^{7--3}=p^{10}\)

\(x^2⋅x^{-8}=x^{2+-8}=x^{-6}\)

\((x^6)^{-4}=x^{6⋅-4}=x^{-24}\)

\(a^6⋅{1 \over a^8}=a^6⋅a^{-8}=a^{6+-8}=a^{-2}\)

\({({1 \over x^4}) \over x^2}={x^{-4} \over x^2}=x^{-4-2}=x^{-6}\)

\({a^8 \over a^0}=a^{8-0}=a^8\)

\({3 \over a^2}\)

\({5p^5 \over 7p^9}={5 \over 7}⋅{p^5 \over p^9}={5 \over 7}⋅p^{5-9}={5 \over 7}p^{-4}\)

\({x^2 \over ({1 \over x^4})}={x^2 \over x^{-4}}=x^{2--4}=x^6\)

\({8x^3y^5 \over 7xy^6}={8 \over 7}⋅{x^3 \over x^1}⋅{y^5 \over y^6}={8 \over 7}⋅x^{3-1}⋅x^{5-6}=1\frac{1}{7}x^2y^{-1}\)

\(p^7⋅\sqrt[8]{p}=p^7⋅p^{\frac{1}{8}}=p^{7+\frac{1}{8}}=p^{7\frac{1}{8}}\)

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

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

\({1 \over a^6}⋅\sqrt[9]{a^4}=a^{-6}⋅a^{\frac{4}{9}}=a^{-6+\frac{4}{9}}=a^{-5\frac{5}{9}}\)

\({\sqrt[5]{x^2} \over \sqrt[7]{x^2}}={x^{\frac{2}{5}} \over x^{\frac{2}{7}}}=x^{\frac{2}{5}-\frac{2}{7}}=x^{\frac{4}{35}}\)

\(\sqrt[9]{{1 \over x^4}}=\sqrt[9]{x^{-4}}=x^{-\frac{4}{9}}\)

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

\({a^6 \over a^2⋅\sqrt[3]{a^2}}={a^6 \over a^2⋅a^{\frac{2}{3}}}={a^6 \over a^{2\frac{2}{3}}}=a^{6-2\frac{2}{3}}=a^{3\frac{1}{3}}\)

\({3b^9 \over 5a^7}\)

\((3a)^{-4}=3^{-4}⋅a^{-4}={1 \over 3^4}⋅{1 \over a^4}={1 \over 81a^4}\)

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

\(6a^{9\frac{8}{9}}=6⋅a^9⋅a^{\frac{8}{9}}=6a^9⋅\sqrt[9]{a^8}\)

\(\frac{3}{8}a^{-\frac{7}{8}}b^{\frac{1}{6}}=\frac{3}{8}⋅{1 \over a^{\frac{7}{8}}}⋅b^{\frac{1}{6}}={3⋅\sqrt[6]{b} \over 8⋅\sqrt[8]{a^7}}\)