\({1 \over p^{5}} = p^{-5}\)

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

\({a^{4} \over a^{-2}} = a^{4 - -2} = a^{6}\)

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

\((x^{8})^{-6} = x^{8 ⋅ -6} = x^{-48}\)

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

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

\({8 \over x^{9}}\)

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

\(p^{2} ⋅ \sqrt[8]{p} = p^{2} ⋅ p^{\frac{1}{8}} = p^{2 + \frac{1}{8}} = p^{2\frac{1}{8}}\)

\(a^{9} ⋅ \sqrt[8]{a^{7}} = a^{9} ⋅ a^{\frac{7}{8}} = a^{9 + \frac{7}{8}} = a^{9\frac{7}{8}}\)

\({x^{4} \over \sqrt[6]{x^{5}}} = {x^{4} \over x^{\frac{5}{6}}} = x^{4 - \frac{5}{6}} = x^{3\frac{1}{6}}\)

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

\({\sqrt[9]{a^{5}} \over \sqrt[8]{a^{3}}} = {a^{\frac{5}{9}} \over a^{\frac{3}{8}}} = a^{\frac{5}{9} - \frac{3}{8}} = a^{\frac{13}{72}}\)

\(\sqrt{a^{6}} = a^{\frac{6}{2}} = a^{3}\)

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

\(5 x^{6\frac{2}{7}} = 5 ⋅ x^{6} ⋅ x^{\frac{2}{7}} = 5 x^{6} ⋅ \sqrt[7]{x^{2}}\)