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

\({x^{6} \over x^{-5}} = x^{6 - -5} = x^{11}\)

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

\((x^{6})^{-5} = x^{6 ⋅ -5} = x^{-30}\)

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

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

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

\({9 \over a^{4}}\)

\({3 x^{5} \over 7 x^{9}} = {3 \over 7} ⋅ {x^{5} \over x^{9}} = {3 \over 7} ⋅ x^{5 - 9} = {3 \over 7} x^{-4}\)

\({a^{2} \over ({1 \over a^{3}})} = {a^{2} \over a^{-3}} = a^{2 - -3} = a^{5}\)

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

\(x^{5} ⋅ \sqrt{x} = x^{5} ⋅ x^{\frac{1}{2}} = x^{5 + \frac{1}{2}} = x^{5\frac{1}{2}}\)

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

\({x^{2} \over \sqrt[6]{x^{5}}} = {x^{2} \over x^{\frac{5}{6}}} = x^{2 - \frac{5}{6}} = x^{1\frac{1}{6}}\)

\({1 \over a^{6}} ⋅ \sqrt[7]{a^{4}} = a^{-6} ⋅ a^{\frac{4}{7}} = a^{-6 + \frac{4}{7}} = a^{-5\frac{3}{7}}\)

\({\sqrt[3]{x^{2}} \over \sqrt[7]{x^{4}}} = {x^{\frac{2}{3}} \over x^{\frac{4}{7}}} = x^{\frac{2}{3} - \frac{4}{7}} = x^{\frac{2}{21}}\)

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

\(\sqrt{a^{8}} = a^{\frac{8}{2}} = a^{4}\)

\({x^{7} \over x^{8} ⋅ \sqrt[7]{x^{6}}} = {x^{7} \over x^{8} ⋅ x^{\frac{6}{7}}} = {x^{7} \over x^{8\frac{6}{7}}} = x^{7 - 8\frac{6}{7}} = x^{-1\frac{6}{7}}\)

\({7 q^{8} \over 8 p^{9}}\)

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

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

\(9 p^{6\frac{3}{7}} = 9 ⋅ p^{6} ⋅ p^{\frac{3}{7}} = 9 p^{6} ⋅ \sqrt[7]{p^{3}}\)

\(\frac{1}{8} x^{-\frac{8}{9}} y^{\frac{3}{7}} = \frac{1}{8} ⋅ {1 \over x^{\frac{8}{9}}} ⋅ y^{\frac{3}{7}} = {1 ⋅ \sqrt[7]{y^{3}} \over 8 ⋅ \sqrt[9]{x^{8}}}\)