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

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

\(x^{5} ⋅ x^{-8} = x^{5 + -8} = x^{-3}\)

\((a^{2})^{-9} = a^{2 ⋅ -9} = a^{-18}\)

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

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

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

\({3 \over x^{2}}\)

\({3 p^{3} \over 4 p^{5}} = {3 \over 4} ⋅ {p^{3} \over p^{5}} = {3 \over 4} ⋅ p^{3 - 5} = {3 \over 4} p^{-2}\)

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

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

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

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

\({a^{3} \over \sqrt[9]{a^{8}}} = {a^{3} \over a^{\frac{8}{9}}} = a^{3 - \frac{8}{9}} = a^{2\frac{1}{9}}\)

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

\({\sqrt[7]{a^{5}} \over \sqrt[5]{a^{2}}} = {a^{\frac{5}{7}} \over a^{\frac{2}{5}}} = a^{\frac{5}{7} - \frac{2}{5}} = a^{\frac{11}{35}}\)

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

\(\sqrt[5]{x^{25}} = x^{\frac{25}{5}} = x^{5}\)

\({x^{4} \over x^{6} ⋅ \sqrt[8]{x^{3}}} = {x^{4} \over x^{6} ⋅ x^{\frac{3}{8}}} = {x^{4} \over x^{6\frac{3}{8}}} = x^{4 - 6\frac{3}{8}} = x^{-2\frac{3}{8}}\)

\({8 y^{9} \over 9 x^{6}}\)

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

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

\(9 p^{2\frac{6}{7}} = 9 ⋅ p^{2} ⋅ p^{\frac{6}{7}} = 9 p^{2} ⋅ \sqrt[7]{p^{6}}\)

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