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

\({x^{8} \over x^{-6}} = x^{8 - -6} = x^{14}\)

\(a^{2} ⋅ a^{-8} = a^{2 + -8} = a^{-6}\)

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

\(a^{2} ⋅ {1 \over a^{8}} = a^{2} ⋅ a^{-8} = a^{2 + -8} = a^{-6}\)

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

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

\({2 \over x^{5}}\)

\({7 x^{3} \over 9 x^{6}} = {7 \over 9} ⋅ {x^{3} \over x^{6}} = {7 \over 9} ⋅ x^{3 - 6} = {7 \over 9} x^{-3}\)

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

\({7 p^{7} q^{4} \over 3 p^{2} q^{8}} = {7 \over 3} ⋅ {p^{7} \over p^{2}} ⋅ {q^{4} \over q^{8}} = {7 \over 3} ⋅ p^{7 - 2} ⋅ p^{4 - 8} = 2\frac{1}{3} p^{5} q^{-4}\)

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

\(a^{6} ⋅ \sqrt[5]{a^{2}} = a^{6} ⋅ a^{\frac{2}{5}} = a^{6 + \frac{2}{5}} = a^{6\frac{2}{5}}\)

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

\({1 \over x^{8}} ⋅ \sqrt[9]{x^{7}} = x^{-8} ⋅ x^{\frac{7}{9}} = x^{-8 + \frac{7}{9}} = x^{-7\frac{2}{9}}\)

\({\sqrt[5]{a^{2}} \over \sqrt[8]{a^{3}}} = {a^{\frac{2}{5}} \over a^{\frac{3}{8}}} = a^{\frac{2}{5} - \frac{3}{8}} = a^{\frac{1}{40}}\)

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

\(\sqrt{x^{6}} = x^{\frac{6}{2}} = x^{3}\)

\({a^{5} \over a^{4} ⋅ \sqrt[5]{a^{2}}} = {a^{5} \over a^{4} ⋅ a^{\frac{2}{5}}} = {a^{5} \over a^{4\frac{2}{5}}} = a^{5 - 4\frac{2}{5}} = a^{\frac{3}{5}}\)

\({5 y^{8} \over 9 x^{9}}\)

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

\(({1 \over 5} p)^{-2} = (5^{-1} ⋅ p)^{-2} = (5^{-1})^{-2} ⋅ p^{-2} = 5^{2} ⋅ p^{-2} = {25 \over p^{2}}\)

\(5 p^{9\frac{6}{7}} = 5 ⋅ p^{9} ⋅ p^{\frac{6}{7}} = 5 p^{9} ⋅ \sqrt[7]{p^{6}}\)

\(\frac{1}{2} a^{-\frac{5}{7}} b^{\frac{4}{5}} = \frac{1}{2} ⋅ {1 \over a^{\frac{5}{7}}} ⋅ b^{\frac{4}{5}} = {1 ⋅ \sqrt[5]{b^{4}} \over 2 ⋅ \sqrt[7]{a^{5}}}\)