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

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

\(x^{4} ⋅ x^{-5} = x^{4 + -5} = x^{-1}\)

\((x^{8})^{-4} = x^{8 ⋅ -4} = x^{-32}\)

\(a^{7} ⋅ {1 \over a^{8}} = a^{7} ⋅ a^{-8} = a^{7 + -8} = a^{-1}\)

\({({1 \over a^{6}}) \over a^{4}} = {a^{-6} \over a^{4}} = a^{-6 - 4} = a^{-10}\)

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

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

\({5 a^{5} \over 9 a^{6}} = {5 \over 9} ⋅ {a^{5} \over a^{6}} = {5 \over 9} ⋅ a^{5 - 6} = {5 \over 9} a^{-1}\)

\({p^{2} \over ({1 \over p^{6}})} = {p^{2} \over p^{-6}} = p^{2 - -6} = p^{8}\)

\({4 a^{8} b^{2} \over 3 a^{4} b^{5}} = {4 \over 3} ⋅ {a^{8} \over a^{4}} ⋅ {b^{2} \over b^{5}} = {4 \over 3} ⋅ a^{8 - 4} ⋅ a^{2 - 5} = 1\frac{1}{3} a^{4} b^{-3}\)

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

\(a^{7} ⋅ \sqrt[5]{a^{2}} = a^{7} ⋅ a^{\frac{2}{5}} = a^{7 + \frac{2}{5}} = a^{7\frac{2}{5}}\)

\({x^{3} \over \sqrt[7]{x^{3}}} = {x^{3} \over x^{\frac{3}{7}}} = x^{3 - \frac{3}{7}} = x^{2\frac{4}{7}}\)

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

\({\sqrt[9]{a^{8}} \over \sqrt[9]{a^{2}}} = {a^{\frac{8}{9}} \over a^{\frac{2}{9}}} = a^{\frac{8}{9} - \frac{2}{9}} = a^{\frac{2}{3}}\)

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

\(\sqrt[3]{x^{15}} = x^{\frac{15}{3}} = x^{5}\)

\({a^{5} \over a^{6} ⋅ \sqrt[7]{a^{6}}} = {a^{5} \over a^{6} ⋅ a^{\frac{6}{7}}} = {a^{5} \over a^{6\frac{6}{7}}} = a^{5 - 6\frac{6}{7}} = a^{-1\frac{6}{7}}\)

\({3 y^{5} \over 4 x^{2}}\)

\((4 a)^{-5} = 4^{-5} ⋅ a^{-5} = {1 \over 4^{5}} ⋅ {1 \over a^{5}} = {1 \over 1\,024 a^{5}}\)

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

\(9 p^{6\frac{5}{9}} = 9 ⋅ p^{6} ⋅ p^{\frac{5}{9}} = 9 p^{6} ⋅ \sqrt[9]{p^{5}}\)

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