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

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

\(x^8⋅x^{-9}=x^{8+-9}=x^{-1}\)

\((a^6)^{-2}=a^{6⋅-2}=a^{-12}\)

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

\({({1 \over p^4}) \over p^2}={p^{-4} \over p^2}=p^{-4-2}=p^{-6}\)

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

\({6 \over x^3}\)

\({3p^4 \over 7p^7}={3 \over 7}⋅{p^4 \over p^7}={3 \over 7}⋅p^{4-7}={3 \over 7}p^{-3}\)

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

\({9p^3q^2 \over 8pq^5}={9 \over 8}⋅{p^3 \over p^1}⋅{q^2 \over q^5}={9 \over 8}⋅p^{3-1}⋅p^{2-5}=1\frac{1}{8}p^2q^{-3}\)

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

\(x^6⋅\sqrt[9]{x^5}=x^6⋅x^{\frac{5}{9}}=x^{6+\frac{5}{9}}=x^{6\frac{5}{9}}\)

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

\({1 \over a^6}⋅\sqrt[5]{a^3}=a^{-6}⋅a^{\frac{3}{5}}=a^{-6+\frac{3}{5}}=a^{-5\frac{2}{5}}\)

\({\sqrt[8]{x^3} \over \sqrt[9]{x^2}}={x^{\frac{3}{8}} \over x^{\frac{2}{9}}}=x^{\frac{3}{8}-\frac{2}{9}}=x^{\frac{11}{72}}\)

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

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

\({a^5 \over a^8⋅\sqrt[7]{a^2}}={a^5 \over a^8⋅a^{\frac{2}{7}}}={a^5 \over a^{8\frac{2}{7}}}=a^{5-8\frac{2}{7}}=a^{-3\frac{2}{7}}\)

\({2b^8 \over 9a^5}\)

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

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

\(8x^{4\frac{5}{6}}=8⋅x^4⋅x^{\frac{5}{6}}=8x^4⋅\sqrt[6]{x^5}\)

\(\frac{1}{3}x^{-\frac{6}{7}}y^{\frac{5}{6}}=\frac{1}{3}⋅{1 \over x^{\frac{6}{7}}}⋅y^{\frac{5}{6}}={1⋅\sqrt[6]{y^5} \over 3⋅\sqrt[7]{x^6}}\)