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

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

\({a^{6} \over a^{-2}} = a^{6 - -2} = a^{8}\)

\(x^{2} ⋅ x^{-8} = x^{2 + -8} = x^{-6}\)

\((a^{9})^{-6} = a^{9 ⋅ -6} = a^{-54}\)

\(p^{5} ⋅ {1 \over p^{9}} = p^{5} ⋅ p^{-9} = p^{5 + -9} = p^{-4}\)

\({x^{0} \over x^{8}} = x^{0 - 8} = x^{-8}\)

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

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

\(x^{8} ⋅ \sqrt[5]{x} = x^{8} ⋅ x^{\frac{1}{5}} = x^{8 + \frac{1}{5}} = x^{8\frac{1}{5}}\)

\(x^{4} ⋅ \sqrt[8]{x^{3}} = x^{4} ⋅ x^{\frac{3}{8}} = x^{4 + \frac{3}{8}} = x^{4\frac{3}{8}}\)

\({a^{3} \over \sqrt[6]{a^{5}}} = {a^{3} \over a^{\frac{5}{6}}} = a^{3 - \frac{5}{6}} = a^{2\frac{1}{6}}\)

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

\({\sqrt[7]{p^{5}} \over \sqrt[5]{p^{3}}} = {p^{\frac{5}{7}} \over p^{\frac{3}{5}}} = p^{\frac{5}{7} - \frac{3}{5}} = p^{\frac{4}{35}}\)

\(\sqrt[5]{a^{10}} = a^{\frac{10}{5}} = a^{2}\)

\({p^{2} \over p^{3} ⋅ \sqrt[5]{p^{3}}} = {p^{2} \over p^{3} ⋅ p^{\frac{3}{5}}} = {p^{2} \over p^{3\frac{3}{5}}} = p^{2 - 3\frac{3}{5}} = p^{-1\frac{3}{5}}\)

\(7 x^{3\frac{3}{5}} = 7 ⋅ x^{3} ⋅ x^{\frac{3}{5}} = 7 x^{3} ⋅ \sqrt[5]{x^{3}}\)