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

\({p^7 \over p^{-4}}=p^{7--4}=p^{11}\)

\(x^6⋅x^{-8}=x^{6+-8}=x^{-2}\)

\((x^3)^{-9}=x^{3⋅-9}=x^{-27}\)

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

\({({1 \over a^7}) \over a^6}={a^{-7} \over a^6}=a^{-7-6}=a^{-13}\)

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

\({7 \over x^4}\)

\({8a^3 \over 9a^7}={8 \over 9}⋅{a^3 \over a^7}={8 \over 9}⋅a^{3-7}={8 \over 9}a^{-4}\)

\({p^4 \over ({1 \over p^6})}={p^4 \over p^{-6}}=p^{4--6}=p^{10}\)

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

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

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

\({p^6 \over \sqrt[7]{p^2}}={p^6 \over p^{\frac{2}{7}}}=p^{6-\frac{2}{7}}=p^{5\frac{5}{7}}\)

\({1 \over x^7}⋅\sqrt[3]{x^2}=x^{-7}⋅x^{\frac{2}{3}}=x^{-7+\frac{2}{3}}=x^{-6\frac{1}{3}}\)

\({\sqrt[3]{p^2} \over \sqrt[7]{p^2}}={p^{\frac{2}{3}} \over p^{\frac{2}{7}}}=p^{\frac{2}{3}-\frac{2}{7}}=p^{\frac{8}{21}}\)

\(\sqrt[6]{{1 \over x^5}}=\sqrt[6]{x^{-5}}=x^{-\frac{5}{6}}\)

\(\sqrt[3]{a^6}=a^{\frac{6}{3}}=a^2\)

\({x^8 \over x^5⋅\sqrt[7]{x^6}}={x^8 \over x^5⋅x^{\frac{6}{7}}}={x^8 \over x^{5\frac{6}{7}}}=x^{8-5\frac{6}{7}}=x^{2\frac{1}{7}}\)

\({5y^3 \over 8x^8}\)

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

\(({1 \over 2}a)^{-4}=(2^{-1}⋅a)^{-4}=(2^{-1})^{-4}⋅a^{-4}=2^4⋅a^{-4}={16 \over a^4}\)

\(6a^{5\frac{3}{4}}=6⋅a^5⋅a^{\frac{3}{4}}=6a^5⋅\sqrt[4]{a^3}\)

\(\frac{5}{9}a^{-\frac{1}{9}}b^{\frac{2}{9}}=\frac{5}{9}⋅{1 \over a^{\frac{1}{9}}}⋅b^{\frac{2}{9}}={5⋅\sqrt[9]{b^2} \over 9⋅\sqrt[9]{a}}\)