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

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

\(p^{2} ⋅ p^{-4} = p^{2 + -4} = p^{-2}\)

\((x^{6})^{-7} = x^{6 ⋅ -7} = x^{-42}\)

\(a^{3} ⋅ {1 \over a^{7}} = a^{3} ⋅ a^{-7} = a^{3 + -7} = a^{-4}\)

\({({1 \over a^{6}}) \over a^{5}} = {a^{-6} \over a^{5}} = a^{-6 - 5} = a^{-11}\)

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

\({8 \over p^{3}}\)

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

\({x^{6} \over ({1 \over x^{8}})} = {x^{6} \over x^{-8}} = x^{6 - -8} = x^{14}\)

\({6 p^{5} q \over 5 p^{4} q^{4}} = {6 \over 5} ⋅ {p^{5} \over p^{4}} ⋅ {q^{1} \over q^{4}} = {6 \over 5} ⋅ p^{5 - 4} ⋅ p^{1 - 4} = 1\frac{1}{5} p q^{-3}\)

\(x^{3} ⋅ \sqrt[9]{x} = x^{3} ⋅ x^{\frac{1}{9}} = x^{3 + \frac{1}{9}} = x^{3\frac{1}{9}}\)

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

\({x^{7} \over \sqrt[5]{x^{3}}} = {x^{7} \over x^{\frac{3}{5}}} = x^{7 - \frac{3}{5}} = x^{6\frac{2}{5}}\)

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

\({\sqrt[7]{x^{4}} \over \sqrt[8]{x^{3}}} = {x^{\frac{4}{7}} \over x^{\frac{3}{8}}} = x^{\frac{4}{7} - \frac{3}{8}} = x^{\frac{11}{56}}\)

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

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

\({p^{6} \over p^{9} ⋅ \sqrt[9]{p^{4}}} = {p^{6} \over p^{9} ⋅ p^{\frac{4}{9}}} = {p^{6} \over p^{9\frac{4}{9}}} = p^{6 - 9\frac{4}{9}} = p^{-3\frac{4}{9}}\)

\({4 b^{5} \over 9 a^{9}}\)

\((4 x)^{-3} = 4^{-3} ⋅ x^{-3} = {1 \over 4^{3}} ⋅ {1 \over x^{3}} = {1 \over 64 x^{3}}\)

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

\(5 a^{6\frac{3}{5}} = 5 ⋅ a^{6} ⋅ a^{\frac{3}{5}} = 5 a^{6} ⋅ \sqrt[5]{a^{3}}\)

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