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

\({a^2 \over a^{-8}}=a^{2--8}=a^{10}\)

\(p^2⋅p^{-6}=p^{2+-6}=p^{-4}\)

\((x^6)^{-4}=x^{6⋅-4}=x^{-24}\)

\(a^5⋅{1 \over a^9}=a^5⋅a^{-9}=a^{5+-9}=a^{-4}\)

\({({1 \over x^6}) \over x^3}={x^{-6} \over x^3}=x^{-6-3}=x^{-9}\)

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

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

\({2x^4 \over 7x^9}={2 \over 7}⋅{x^4 \over x^9}={2 \over 7}⋅x^{4-9}={2 \over 7}x^{-5}\)

\({a^5 \over ({1 \over a^9})}={a^5 \over a^{-9}}=a^{5--9}=a^{14}\)

\({8x^5y^3 \over 5x^4y^5}={8 \over 5}⋅{x^5 \over x^4}⋅{y^3 \over y^5}={8 \over 5}⋅x^{5-4}⋅x^{3-5}=1\frac{3}{5}xy^{-2}\)

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

\(a^3⋅\sqrt[8]{a^7}=a^3⋅a^{\frac{7}{8}}=a^{3+\frac{7}{8}}=a^{3\frac{7}{8}}\)

\({a^5 \over \sqrt[9]{a^7}}={a^5 \over a^{\frac{7}{9}}}=a^{5-\frac{7}{9}}=a^{4\frac{2}{9}}\)

\({1 \over x^4}⋅\sqrt[9]{x^4}=x^{-4}⋅x^{\frac{4}{9}}=x^{-4+\frac{4}{9}}=x^{-3\frac{5}{9}}\)

\({\sqrt[9]{x^4} \over \sqrt[5]{x^2}}={x^{\frac{4}{9}} \over x^{\frac{2}{5}}}=x^{\frac{4}{9}-\frac{2}{5}}=x^{\frac{2}{45}}\)

\(\sqrt[9]{{1 \over x^8}}=\sqrt[9]{x^{-8}}=x^{-\frac{8}{9}}\)

\(\sqrt[5]{a^{25}}=a^{\frac{25}{5}}=a^5\)

\({p^9 \over p^8⋅\sqrt[9]{p^7}}={p^9 \over p^8⋅p^{\frac{7}{9}}}={p^9 \over p^{8\frac{7}{9}}}=p^{9-8\frac{7}{9}}=p^{\frac{2}{9}}\)

\({6y^9 \over 7x^5}\)

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

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

\(7a^{3\frac{7}{8}}=7⋅a^3⋅a^{\frac{7}{8}}=7a^3⋅\sqrt[8]{a^7}\)

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