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

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

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

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

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

\({({1 \over x^{8}}) \over x^{2}} = {x^{-8} \over x^{2}} = x^{-8 - 2} = x^{-10}\)

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

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

\({2 x^{5} \over 7 x^{6}} = {2 \over 7} ⋅ {x^{5} \over x^{6}} = {2 \over 7} ⋅ x^{5 - 6} = {2 \over 7} x^{-1}\)

\({x^{3} \over ({1 \over x^{6}})} = {x^{3} \over x^{-6}} = x^{3 - -6} = x^{9}\)

\({7 a^{7} b^{2} \over 5 a^{3} b^{6}} = {7 \over 5} ⋅ {a^{7} \over a^{3}} ⋅ {b^{2} \over b^{6}} = {7 \over 5} ⋅ a^{7 - 3} ⋅ a^{2 - 6} = 1\frac{2}{5} a^{4} b^{-4}\)

\(x^{2} ⋅ \sqrt[3]{x} = x^{2} ⋅ x^{\frac{1}{3}} = x^{2 + \frac{1}{3}} = x^{2\frac{1}{3}}\)

\(x^{9} ⋅ \sqrt[7]{x^{5}} = x^{9} ⋅ x^{\frac{5}{7}} = x^{9 + \frac{5}{7}} = x^{9\frac{5}{7}}\)

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

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

\({\sqrt[8]{x^{7}} \over \sqrt[9]{x^{4}}} = {x^{\frac{7}{8}} \over x^{\frac{4}{9}}} = x^{\frac{7}{8} - \frac{4}{9}} = x^{\frac{31}{72}}\)

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

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

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

\({5 b^{9} \over 7 a^{2}}\)

\((5 p)^{-3} = 5^{-3} ⋅ p^{-3} = {1 \over 5^{3}} ⋅ {1 \over p^{3}} = {1 \over 125 p^{3}}\)

\(({1 \over 2} a)^{-5} = (2^{-1} ⋅ a)^{-5} = (2^{-1})^{-5} ⋅ a^{-5} = 2^{5} ⋅ a^{-5} = {32 \over a^{5}}\)

\(5 p^{4\frac{5}{7}} = 5 ⋅ p^{4} ⋅ p^{\frac{5}{7}} = 5 p^{4} ⋅ \sqrt[7]{p^{5}}\)

\(\frac{5}{6} a^{-\frac{5}{9}} b^{\frac{8}{9}} = \frac{5}{6} ⋅ {1 \over a^{\frac{5}{9}}} ⋅ b^{\frac{8}{9}} = {5 ⋅ \sqrt[9]{b^{8}} \over 6 ⋅ \sqrt[9]{a^{5}}}\)