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

\({3 a^{3} \over 8 a^{8}} = {3 \over 8} ⋅ {a^{3} \over a^{8}} = {3 \over 8} ⋅ a^{3 - 8} = {3 \over 8} a^{-5}\)

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

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

\((p^{3})^{-8} = p^{3 ⋅ -8} = p^{-24}\)

\(p^{3} ⋅ {1 \over p^{8}} = p^{3} ⋅ p^{-8} = p^{3 + -8} = p^{-5}\)

\({a^{5} \over a^{0}} = a^{5 - 0} = a^{5}\)

\({3 \over x^{2}}\)

\((5 a)^{-4} = 5^{-4} ⋅ a^{-4} = {1 \over 5^{4}} ⋅ {1 \over a^{4}} = {1 \over 625 a^{4}}\)

\(a^{8} ⋅ \sqrt[6]{a} = a^{8} ⋅ a^{\frac{1}{6}} = a^{8 + \frac{1}{6}} = a^{8\frac{1}{6}}\)

\(x^{8} ⋅ \sqrt[7]{x^{6}} = x^{8} ⋅ x^{\frac{6}{7}} = x^{8 + \frac{6}{7}} = x^{8\frac{6}{7}}\)

\({p^{8} \over \sqrt[9]{p^{4}}} = {p^{8} \over p^{\frac{4}{9}}} = p^{8 - \frac{4}{9}} = p^{7\frac{5}{9}}\)

\({1 \over a^{5}} ⋅ \sqrt[3]{a^{2}} = a^{-5} ⋅ a^{\frac{2}{3}} = a^{-5 + \frac{2}{3}} = a^{-4\frac{1}{3}}\)

\({\sqrt[5]{x^{4}} \over \sqrt[9]{x^{2}}} = {x^{\frac{4}{5}} \over x^{\frac{2}{9}}} = x^{\frac{4}{5} - \frac{2}{9}} = x^{\frac{26}{45}}\)

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

\({a^{4} \over a^{9} ⋅ \sqrt[9]{a^{8}}} = {a^{4} \over a^{9} ⋅ a^{\frac{8}{9}}} = {a^{4} \over a^{9\frac{8}{9}}} = a^{4 - 9\frac{8}{9}} = a^{-5\frac{8}{9}}\)

\(8 p^{9\frac{2}{7}} = 8 ⋅ p^{9} ⋅ p^{\frac{2}{7}} = 8 p^{9} ⋅ \sqrt[7]{p^{2}}\)