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

\({x^{9} \over x^{-6}} = x^{9 - -6} = x^{15}\)

\(x^{2} ⋅ x^{-7} = x^{2 + -7} = x^{-5}\)

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

\(a^{4} ⋅ {1 \over a^{6}} = a^{4} ⋅ a^{-6} = a^{4 + -6} = a^{-2}\)

\({({1 \over x^{5}}) \over x^{3}} = {x^{-5} \over x^{3}} = x^{-5 - 3} = x^{-8}\)

\({p^{0} \over p^{6}} = p^{0 - 6} = p^{-6}\)

\({6 \over a^{5}}\)

\({5 a^{2} \over 9 a^{7}} = {5 \over 9} ⋅ {a^{2} \over a^{7}} = {5 \over 9} ⋅ a^{2 - 7} = {5 \over 9} a^{-5}\)

\({x^{3} \over ({1 \over x^{9}})} = {x^{3} \over x^{-9}} = x^{3 - -9} = x^{12}\)

\({6 x^{2} y^{3} \over 5 x y^{7}} = {6 \over 5} ⋅ {x^{2} \over x^{1}} ⋅ {y^{3} \over y^{7}} = {6 \over 5} ⋅ x^{2 - 1} ⋅ x^{3 - 7} = 1\frac{1}{5} x y^{-4}\)

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

\(x^{5} ⋅ \sqrt[7]{x^{4}} = x^{5} ⋅ x^{\frac{4}{7}} = x^{5 + \frac{4}{7}} = x^{5\frac{4}{7}}\)

\({a^{2} \over \sqrt[9]{a^{7}}} = {a^{2} \over a^{\frac{7}{9}}} = a^{2 - \frac{7}{9}} = a^{1\frac{2}{9}}\)

\({1 \over p^{6}} ⋅ \sqrt[8]{p^{5}} = p^{-6} ⋅ p^{\frac{5}{8}} = p^{-6 + \frac{5}{8}} = p^{-5\frac{3}{8}}\)

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

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

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

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

\({7 q^{3} \over 9 p^{9}}\)

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

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

\(6 a^{9\frac{4}{9}} = 6 ⋅ a^{9} ⋅ a^{\frac{4}{9}} = 6 a^{9} ⋅ \sqrt[9]{a^{4}}\)

\(\frac{3}{4} x^{-\frac{1}{7}} y^{\frac{1}{5}} = \frac{3}{4} ⋅ {1 \over x^{\frac{1}{7}}} ⋅ y^{\frac{1}{5}} = {3 ⋅ \sqrt[5]{y} \over 4 ⋅ \sqrt[7]{x}}\)