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

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

\(a^3⋅a^{-7}=a^{3+-7}=a^{-4}\)

\((x^3)^{-7}=x^{3⋅-7}=x^{-21}\)

\(x^6⋅{1 \over x^7}=x^6⋅x^{-7}=x^{6+-7}=x^{-1}\)

\({({1 \over x^7}) \over x^3}={x^{-7} \over x^3}=x^{-7-3}=x^{-10}\)

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

\({7 \over a^5}\)

\({7a^2 \over 9a^3}={7 \over 9}⋅{a^2 \over a^3}={7 \over 9}⋅a^{2-3}={7 \over 9}a^{-1}\)

\({p^2 \over ({1 \over p^8})}={p^2 \over p^{-8}}=p^{2--8}=p^{10}\)

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

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

\(p^8⋅\sqrt[9]{p^4}=p^8⋅p^{\frac{4}{9}}=p^{8+\frac{4}{9}}=p^{8\frac{4}{9}}\)

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

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

\({\sqrt[8]{a^7} \over \sqrt[4]{a^3}}={a^{\frac{7}{8}} \over a^{\frac{3}{4}}}=a^{\frac{7}{8}-\frac{3}{4}}=a^{\frac{1}{8}}\)

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

\(\sqrt[3]{x^9}=x^{\frac{9}{3}}=x^3\)

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

\({4y^6 \over 5x^4}\)

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

\(({1 \over 2}a)^{-5}=(2^{-1}⋅a)^{-5}=(2^{-1})^{-5}⋅a^{-5}=2^5⋅a^{-5}={32 \over a^5}\)

\(7x^{4\frac{7}{8}}=7⋅x^4⋅x^{\frac{7}{8}}=7x^4⋅\sqrt[8]{x^7}\)

\(\frac{8}{9}x^{-\frac{2}{9}}y^{\frac{6}{7}}=\frac{8}{9}⋅{1 \over x^{\frac{2}{9}}}⋅y^{\frac{6}{7}}={8⋅\sqrt[7]{y^6} \over 9⋅\sqrt[9]{x^2}}\)