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

\({2 x^{3} \over 7 x^{8}} = {2 \over 7} ⋅ {x^{3} \over x^{8}} = {2 \over 7} ⋅ x^{3 - 8} = {2 \over 7} x^{-5}\)

\({a^{6} \over a^{-8}} = a^{6 - -8} = a^{14}\)

\(p^{3} ⋅ p^{-9} = p^{3 + -9} = p^{-6}\)

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

\(x^{3} ⋅ {1 \over x^{4}} = x^{3} ⋅ x^{-4} = x^{3 + -4} = x^{-1}\)

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

\({4 \over a^{7}}\)

\((4 p)^{-3} = 4^{-3} ⋅ p^{-3} = {1 \over 4^{3}} ⋅ {1 \over p^{3}} = {1 \over 64 p^{3}}\)

\(x^{4} ⋅ \sqrt[9]{x} = x^{4} ⋅ x^{\frac{1}{9}} = x^{4 + \frac{1}{9}} = x^{4\frac{1}{9}}\)

\(a^{9} ⋅ \sqrt[9]{a^{2}} = a^{9} ⋅ a^{\frac{2}{9}} = a^{9 + \frac{2}{9}} = a^{9\frac{2}{9}}\)

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

\({1 \over a^{4}} ⋅ \sqrt[7]{a^{5}} = a^{-4} ⋅ a^{\frac{5}{7}} = a^{-4 + \frac{5}{7}} = a^{-3\frac{2}{7}}\)

\({\sqrt[9]{x^{5}} \over \sqrt[9]{x^{4}}} = {x^{\frac{5}{9}} \over x^{\frac{4}{9}}} = x^{\frac{5}{9} - \frac{4}{9}} = x^{\frac{1}{9}}\)

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

\({a^{7} \over a^{2} ⋅ \sqrt[8]{a^{7}}} = {a^{7} \over a^{2} ⋅ a^{\frac{7}{8}}} = {a^{7} \over a^{2\frac{7}{8}}} = a^{7 - 2\frac{7}{8}} = a^{4\frac{1}{8}}\)

\(2 x^{4\frac{8}{9}} = 2 ⋅ x^{4} ⋅ x^{\frac{8}{9}} = 2 x^{4} ⋅ \sqrt[9]{x^{8}}\)