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

\({2 x^{4} \over 5 x^{6}} = {2 \over 5} ⋅ {x^{4} \over x^{6}} = {2 \over 5} ⋅ x^{4 - 6} = {2 \over 5} x^{-2}\)

\({a^{6} \over a^{-7}} = a^{6 - -7} = a^{13}\)

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

\((a^{8})^{-2} = a^{8 ⋅ -2} = a^{-16}\)

\(a^{2} ⋅ {1 \over a^{8}} = a^{2} ⋅ a^{-8} = a^{2 + -8} = a^{-6}\)

\({x^{2} \over x^{0}} = x^{2 - 0} = x^{2}\)

\({8 \over p^{6}}\)

\((2 x)^{-4} = 2^{-4} ⋅ x^{-4} = {1 \over 2^{4}} ⋅ {1 \over x^{4}} = {1 \over 16 x^{4}}\)

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

\(a^{3} ⋅ \sqrt[3]{a^{2}} = a^{3} ⋅ a^{\frac{2}{3}} = a^{3 + \frac{2}{3}} = a^{3\frac{2}{3}}\)

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

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

\({\sqrt[3]{p^{2}} \over \sqrt[8]{p^{3}}} = {p^{\frac{2}{3}} \over p^{\frac{3}{8}}} = p^{\frac{2}{3} - \frac{3}{8}} = p^{\frac{7}{24}}\)

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

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

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