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

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

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

\((a^{6})^{-8} = a^{6 ⋅ -8} = a^{-48}\)

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

\({({1 \over a^{9}}) \over a^{4}} = {a^{-9} \over a^{4}} = a^{-9 - 4} = a^{-13}\)

\({x^{4} \over x^{0}} = x^{4 - 0} = x^{4}\)

\({3 \over a^{4}}\)

\({4 x \over 7 x^{6}} = {4 \over 7} ⋅ {x \over x^{6}} = {4 \over 7} ⋅ x^{1 - 6} = {4 \over 7} x^{-5}\)

\({p^{2} \over ({1 \over p^{9}})} = {p^{2} \over p^{-9}} = p^{2 - -9} = p^{11}\)

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

\(a^{3} ⋅ \sqrt[4]{a} = a^{3} ⋅ a^{\frac{1}{4}} = a^{3 + \frac{1}{4}} = a^{3\frac{1}{4}}\)

\(x^{4} ⋅ \sqrt[3]{x^{2}} = x^{4} ⋅ x^{\frac{2}{3}} = x^{4 + \frac{2}{3}} = x^{4\frac{2}{3}}\)

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

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

\({\sqrt[9]{x^{5}} \over \sqrt[9]{x^{4}}} = {x^{\frac{5}{9}} \over x^{\frac{4}{9}}} = x^{\frac{5}{9} - \frac{4}{9}} = x^{\frac{1}{9}}\)

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

\(\sqrt[4]{a^{20}} = a^{\frac{20}{4}} = a^{5}\)

\({p^{9} \over p^{7} ⋅ \sqrt[7]{p^{6}}} = {p^{9} \over p^{7} ⋅ p^{\frac{6}{7}}} = {p^{9} \over p^{7\frac{6}{7}}} = p^{9 - 7\frac{6}{7}} = p^{1\frac{1}{7}}\)

\({3 b^{9} \over 5 a^{3}}\)

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

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

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

\(\frac{1}{4} a^{-\frac{4}{9}} b^{\frac{3}{8}} = \frac{1}{4} ⋅ {1 \over a^{\frac{4}{9}}} ⋅ b^{\frac{3}{8}} = {1 ⋅ \sqrt[8]{b^{3}} \over 4 ⋅ \sqrt[9]{a^{4}}}\)