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

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

\({a^{4} \over a^{-6}} = a^{4 - -6} = a^{10}\)

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

\((x^{9})^{-8} = x^{9 ⋅ -8} = x^{-72}\)

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

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

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

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

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

\(x^{7} ⋅ \sqrt[9]{x^{5}} = x^{7} ⋅ x^{\frac{5}{9}} = x^{7 + \frac{5}{9}} = x^{7\frac{5}{9}}\)

\({a^{8} \over \sqrt[7]{a^{5}}} = {a^{8} \over a^{\frac{5}{7}}} = a^{8 - \frac{5}{7}} = a^{7\frac{2}{7}}\)

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

\({\sqrt[9]{a^{8}} \over \sqrt[5]{a^{3}}} = {a^{\frac{8}{9}} \over a^{\frac{3}{5}}} = a^{\frac{8}{9} - \frac{3}{5}} = a^{\frac{13}{45}}\)

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

\({a^{2} \over a^{6} ⋅ \sqrt[8]{a^{7}}} = {a^{2} \over a^{6} ⋅ a^{\frac{7}{8}}} = {a^{2} \over a^{6\frac{7}{8}}} = a^{2 - 6\frac{7}{8}} = a^{-4\frac{7}{8}}\)

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