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

\({2x^3 \over 7x^4}={2 \over 7}⋅{x^3 \over x^4}={2 \over 7}⋅x^{3-4}={2 \over 7}x^{-1}\)

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

\(x^4⋅x^{-8}=x^{4+-8}=x^{-4}\)

\((a^7)^{-9}=a^{7⋅-9}=a^{-63}\)

\(a^5⋅{1 \over a^6}=a^5⋅a^{-6}=a^{5+-6}=a^{-1}\)

\({({1 \over x^5}) \over x^4}={x^{-5} \over x^4}=x^{-5-4}=x^{-9}\)

\({p^4 \over ({1 \over p^8})}={p^4 \over p^{-8}}=p^{4--8}=p^{12}\)

\({8p^9q^3 \over 3p^4q^5}={8 \over 3}⋅{p^9 \over p^4}⋅{q^3 \over q^5}={8 \over 3}⋅p^{9-4}⋅p^{3-5}=2\frac{2}{3}p^5q^{-2}\)

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

\(x^4⋅\sqrt[8]{x}=x^4⋅x^{\frac{1}{8}}=x^{4+\frac{1}{8}}=x^{4\frac{1}{8}}\)

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

\({a^3 \over \sqrt[7]{a^3}}={a^3 \over a^{\frac{3}{7}}}=a^{3-\frac{3}{7}}=a^{2\frac{4}{7}}\)

\({1 \over x^9}⋅\sqrt[8]{x^3}=x^{-9}⋅x^{\frac{3}{8}}=x^{-9+\frac{3}{8}}=x^{-8\frac{5}{8}}\)

\({\sqrt[4]{a^3} \over \sqrt[8]{a^5}}={a^{\frac{3}{4}} \over a^{\frac{5}{8}}}=a^{\frac{3}{4}-\frac{5}{8}}=a^{\frac{1}{8}}\)

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

\(\sqrt{p^8}=p^{\frac{8}{2}}=p^4\)

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

\({9 \over x^7}\)

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

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

\(9x^{3\frac{4}{9}}=9⋅x^3⋅x^{\frac{4}{9}}=9x^3⋅\sqrt[9]{x^4}\)

\(\frac{1}{2}a^{-\frac{1}{7}}b^{\frac{3}{7}}=\frac{1}{2}⋅{1 \over a^{\frac{1}{7}}}⋅b^{\frac{3}{7}}={1⋅\sqrt[7]{b^3} \over 2⋅\sqrt[7]{a}}\)

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