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

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

\(a^3⋅a^{-9}=a^{3+-9}=a^{-6}\)

\((p^4)^{-2}=p^{4⋅-2}=p^{-8}\)

\(x^8⋅{1 \over x^9}=x^8⋅x^{-9}=x^{8+-9}=x^{-1}\)

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

\({a^7 \over a^0}=a^{7-0}=a^7\)

\({9 \over x^4}\)

\({5p^2 \over 6p^6}={5 \over 6}⋅{p^2 \over p^6}={5 \over 6}⋅p^{2-6}={5 \over 6}p^{-4}\)

\({x^7 \over ({1 \over x^9})}={x^7 \over x^{-9}}=x^{7--9}=x^{16}\)

\({9x^6y^4 \over 8x^4y^9}={9 \over 8}⋅{x^6 \over x^4}⋅{y^4 \over y^9}={9 \over 8}⋅x^{6-4}⋅x^{4-9}=1\frac{1}{8}x^2y^{-5}\)

\(a^5⋅\sqrt{a}=a^5⋅a^{\frac{1}{2}}=a^{5+\frac{1}{2}}=a^{5\frac{1}{2}}\)

\(a^8⋅\sqrt[9]{a^5}=a^8⋅a^{\frac{5}{9}}=a^{8+\frac{5}{9}}=a^{8\frac{5}{9}}\)

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

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

\({\sqrt[6]{p^5} \over \sqrt[5]{p^3}}={p^{\frac{5}{6}} \over p^{\frac{3}{5}}}=p^{\frac{5}{6}-\frac{3}{5}}=p^{\frac{7}{30}}\)

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

\(\sqrt[3]{x^{15}}=x^{\frac{15}{3}}=x^5\)

\({a^6 \over a^2⋅\sqrt[5]{a^2}}={a^6 \over a^2⋅a^{\frac{2}{5}}}={a^6 \over a^{2\frac{2}{5}}}=a^{6-2\frac{2}{5}}=a^{3\frac{3}{5}}\)

\({2b^4 \over 9a^3}\)

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

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

\(9x^{6\frac{7}{8}}=9⋅x^6⋅x^{\frac{7}{8}}=9x^6⋅\sqrt[8]{x^7}\)

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