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

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

\(x^{2} ⋅ x^{-9} = x^{2 + -9} = x^{-7}\)

\((x^{2})^{-4} = x^{2 ⋅ -4} = x^{-8}\)

\(a^{7} ⋅ {1 \over a^{9}} = a^{7} ⋅ a^{-9} = a^{7 + -9} = a^{-2}\)

\({({1 \over p^{7}}) \over p^{5}} = {p^{-7} \over p^{5}} = p^{-7 - 5} = p^{-12}\)

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

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

\({3 x^{4} \over 5 x^{5}} = {3 \over 5} ⋅ {x^{4} \over x^{5}} = {3 \over 5} ⋅ x^{4 - 5} = {3 \over 5} x^{-1}\)

\({x^{5} \over ({1 \over x^{9}})} = {x^{5} \over x^{-9}} = x^{5 - -9} = x^{14}\)

\({9 a^{2} b^{2} \over 5 a b^{5}} = {9 \over 5} ⋅ {a^{2} \over a^{1}} ⋅ {b^{2} \over b^{5}} = {9 \over 5} ⋅ a^{2 - 1} ⋅ a^{2 - 5} = 1\frac{4}{5} a b^{-3}\)

\(x^{7} ⋅ \sqrt[7]{x} = x^{7} ⋅ x^{\frac{1}{7}} = x^{7 + \frac{1}{7}} = x^{7\frac{1}{7}}\)

\(a^{8} ⋅ \sqrt[9]{a^{7}} = a^{8} ⋅ a^{\frac{7}{9}} = a^{8 + \frac{7}{9}} = a^{8\frac{7}{9}}\)

\({x^{6} \over \sqrt[8]{x^{5}}} = {x^{6} \over x^{\frac{5}{8}}} = x^{6 - \frac{5}{8}} = x^{5\frac{3}{8}}\)

\({1 \over p^{9}} ⋅ \sqrt[7]{p^{5}} = p^{-9} ⋅ p^{\frac{5}{7}} = p^{-9 + \frac{5}{7}} = p^{-8\frac{2}{7}}\)

\({\sqrt[5]{p^{4}} \over \sqrt[9]{p^{4}}} = {p^{\frac{4}{5}} \over p^{\frac{4}{9}}} = p^{\frac{4}{5} - \frac{4}{9}} = p^{\frac{16}{45}}\)

\(\sqrt[8]{{1 \over x^{5}}} = \sqrt[8]{x^{-5}} = x^{-\frac{5}{8}}\)

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

\({a^{7} \over a^{9} ⋅ \sqrt[7]{a^{2}}} = {a^{7} \over a^{9} ⋅ a^{\frac{2}{7}}} = {a^{7} \over a^{9\frac{2}{7}}} = a^{7 - 9\frac{2}{7}} = a^{-2\frac{2}{7}}\)

\({2 q^{2} \over 9 p^{9}}\)

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

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

\(7 x^{9\frac{2}{7}} = 7 ⋅ x^{9} ⋅ x^{\frac{2}{7}} = 7 x^{9} ⋅ \sqrt[7]{x^{2}}\)

\(\frac{1}{3} a^{-\frac{1}{9}} b^{\frac{3}{5}} = \frac{1}{3} ⋅ {1 \over a^{\frac{1}{9}}} ⋅ b^{\frac{3}{5}} = {1 ⋅ \sqrt[5]{b^{3}} \over 3 ⋅ \sqrt[9]{a}}\)