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

\({a^{3} \over a^{-7}} = a^{3 - -7} = a^{10}\)

\(x^{5} ⋅ x^{-9} = x^{5 + -9} = x^{-4}\)

\((a^{6})^{-3} = a^{6 ⋅ -3} = a^{-18}\)

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

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

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

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

\({2 a^{5} \over 5 a^{9}} = {2 \over 5} ⋅ {a^{5} \over a^{9}} = {2 \over 5} ⋅ a^{5 - 9} = {2 \over 5} a^{-4}\)

\({x^{3} \over ({1 \over x^{5}})} = {x^{3} \over x^{-5}} = x^{3 - -5} = x^{8}\)

\({7 a^{10} b^{5} \over 2 a^{5} b^{8}} = {7 \over 2} ⋅ {a^{10} \over a^{5}} ⋅ {b^{5} \over b^{8}} = {7 \over 2} ⋅ a^{10 - 5} ⋅ a^{5 - 8} = 3\frac{1}{2} a^{5} b^{-3}\)

\(a^{9} ⋅ \sqrt[8]{a} = a^{9} ⋅ a^{\frac{1}{8}} = a^{9 + \frac{1}{8}} = a^{9\frac{1}{8}}\)

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

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

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

\({\sqrt[6]{p^{5}} \over \sqrt[4]{p^{3}}} = {p^{\frac{5}{6}} \over p^{\frac{3}{4}}} = p^{\frac{5}{6} - \frac{3}{4}} = p^{\frac{1}{12}}\)

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

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

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

\({8 q^{9} \over 9 p^{4}}\)

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

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

\(8 x^{2\frac{8}{9}} = 8 ⋅ x^{2} ⋅ x^{\frac{8}{9}} = 8 x^{2} ⋅ \sqrt[9]{x^{8}}\)

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