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

\({x^{9} \over x^{-4}} = x^{9 - -4} = x^{13}\)

\(a^{3} ⋅ a^{-5} = a^{3 + -5} = a^{-2}\)

\((x^{5})^{-7} = x^{5 ⋅ -7} = x^{-35}\)

\(p^{2} ⋅ {1 \over p^{5}} = p^{2} ⋅ p^{-5} = p^{2 + -5} = p^{-3}\)

\({({1 \over p^{9}}) \over p^{5}} = {p^{-9} \over p^{5}} = p^{-9 - 5} = p^{-14}\)

\({x^{9} \over x^{0}} = x^{9 - 0} = x^{9}\)

\({3 \over a^{5}}\)

\({5 a^{3} \over 8 a^{8}} = {5 \over 8} ⋅ {a^{3} \over a^{8}} = {5 \over 8} ⋅ a^{3 - 8} = {5 \over 8} a^{-5}\)

\({x^{2} \over ({1 \over x^{5}})} = {x^{2} \over x^{-5}} = x^{2 - -5} = x^{7}\)

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

\(x^{7} ⋅ \sqrt[8]{x} = x^{7} ⋅ x^{\frac{1}{8}} = x^{7 + \frac{1}{8}} = x^{7\frac{1}{8}}\)

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

\({a^{4} \over \sqrt[9]{a^{7}}} = {a^{4} \over a^{\frac{7}{9}}} = a^{4 - \frac{7}{9}} = a^{3\frac{2}{9}}\)

\({1 \over p^{9}} ⋅ \sqrt[9]{p^{5}} = p^{-9} ⋅ p^{\frac{5}{9}} = p^{-9 + \frac{5}{9}} = p^{-8\frac{4}{9}}\)

\({\sqrt[8]{a^{7}} \over \sqrt[8]{a^{5}}} = {a^{\frac{7}{8}} \over a^{\frac{5}{8}}} = a^{\frac{7}{8} - \frac{5}{8}} = a^{\frac{1}{4}}\)

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

\(\sqrt[4]{x^{8}} = x^{\frac{8}{4}} = x^{2}\)

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

\({2 q^{6} \over 5 p^{5}}\)

\((4 x)^{-5} = 4^{-5} ⋅ x^{-5} = {1 \over 4^{5}} ⋅ {1 \over x^{5}} = {1 \over 1\,024 x^{5}}\)

\(({1 \over 3} a)^{-5} = (3^{-1} ⋅ a)^{-5} = (3^{-1})^{-5} ⋅ a^{-5} = 3^{5} ⋅ a^{-5} = {243 \over a^{5}}\)

\(7 p^{5\frac{7}{8}} = 7 ⋅ p^{5} ⋅ p^{\frac{7}{8}} = 7 p^{5} ⋅ \sqrt[8]{p^{7}}\)

\(\frac{5}{7} a^{-\frac{1}{5}} b^{\frac{5}{6}} = \frac{5}{7} ⋅ {1 \over a^{\frac{1}{5}}} ⋅ b^{\frac{5}{6}} = {5 ⋅ \sqrt[6]{b^{5}} \over 7 ⋅ \sqrt[5]{a}}\)