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

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

\(a^{3} ⋅ a^{-5} = a^{3 + -5} = a^{-2}\)

\((p^{5})^{-7} = p^{5 ⋅ -7} = p^{-35}\)

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

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

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

\({7 \over a^{2}}\)

\({4 x^{5} \over 9 x^{7}} = {4 \over 9} ⋅ {x^{5} \over x^{7}} = {4 \over 9} ⋅ x^{5 - 7} = {4 \over 9} x^{-2}\)

\({a^{3} \over ({1 \over a^{8}})} = {a^{3} \over a^{-8}} = a^{3 - -8} = a^{11}\)

\({7 x^{8} y \over 6 x^{4} y^{4}} = {7 \over 6} ⋅ {x^{8} \over x^{4}} ⋅ {y^{1} \over y^{4}} = {7 \over 6} ⋅ x^{8 - 4} ⋅ x^{1 - 4} = 1\frac{1}{6} x^{4} y^{-3}\)

\(x^{4} ⋅ \sqrt[6]{x} = x^{4} ⋅ x^{\frac{1}{6}} = x^{4 + \frac{1}{6}} = x^{4\frac{1}{6}}\)

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

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

\({1 \over a^{9}} ⋅ \sqrt[7]{a^{4}} = a^{-9} ⋅ a^{\frac{4}{7}} = a^{-9 + \frac{4}{7}} = a^{-8\frac{3}{7}}\)

\({\sqrt[5]{x^{3}} \over \sqrt[9]{x^{5}}} = {x^{\frac{3}{5}} \over x^{\frac{5}{9}}} = x^{\frac{3}{5} - \frac{5}{9}} = x^{\frac{2}{45}}\)

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

\(\sqrt[5]{a^{25}} = a^{\frac{25}{5}} = a^{5}\)

\({a^{4} \over a^{2} ⋅ \sqrt[7]{a^{4}}} = {a^{4} \over a^{2} ⋅ a^{\frac{4}{7}}} = {a^{4} \over a^{2\frac{4}{7}}} = a^{4 - 2\frac{4}{7}} = a^{1\frac{3}{7}}\)

\({4 y^{2} \over 7 x^{9}}\)

\((3 p)^{-2} = 3^{-2} ⋅ p^{-2} = {1 \over 3^{2}} ⋅ {1 \over p^{2}} = {1 \over 9 p^{2}}\)

\(({1 \over 4} a)^{-5} = (4^{-1} ⋅ a)^{-5} = (4^{-1})^{-5} ⋅ a^{-5} = 4^{5} ⋅ a^{-5} = {1\,024 \over a^{5}}\)

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

\(\frac{1}{7} p^{-\frac{3}{5}} q^{\frac{4}{9}} = \frac{1}{7} ⋅ {1 \over p^{\frac{3}{5}}} ⋅ q^{\frac{4}{9}} = {1 ⋅ \sqrt[9]{q^{4}} \over 7 ⋅ \sqrt[5]{p^{3}}}\)