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

\({x^{9} \over x^{-2}} = x^{9 - -2} = x^{11}\)

\(a^{2} ⋅ a^{-4} = a^{2 + -4} = a^{-2}\)

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

\(a^{8} ⋅ {1 \over a^{9}} = a^{8} ⋅ a^{-9} = a^{8 + -9} = a^{-1}\)

\({({1 \over a^{6}}) \over a^{5}} = {a^{-6} \over a^{5}} = a^{-6 - 5} = a^{-11}\)

\({x^{0} \over x^{7}} = x^{0 - 7} = x^{-7}\)

\({3 \over a^{9}}\)

\({8 p \over 9 p^{2}} = {8 \over 9} ⋅ {p \over p^{2}} = {8 \over 9} ⋅ p^{1 - 2} = {8 \over 9} p^{-1}\)

\({x^{5} \over ({1 \over x^{8}})} = {x^{5} \over x^{-8}} = x^{5 - -8} = x^{13}\)

\({3 a^{6} b^{4} \over 2 a^{2} b^{9}} = {3 \over 2} ⋅ {a^{6} \over a^{2}} ⋅ {b^{4} \over b^{9}} = {3 \over 2} ⋅ a^{6 - 2} ⋅ a^{4 - 9} = 1\frac{1}{2} a^{4} b^{-5}\)

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

\(p^{3} ⋅ \sqrt[7]{p^{2}} = p^{3} ⋅ p^{\frac{2}{7}} = p^{3 + \frac{2}{7}} = p^{3\frac{2}{7}}\)

\({a^{2} \over \sqrt[9]{a^{4}}} = {a^{2} \over a^{\frac{4}{9}}} = a^{2 - \frac{4}{9}} = a^{1\frac{5}{9}}\)

\({1 \over x^{7}} ⋅ \sqrt[9]{x^{8}} = x^{-7} ⋅ x^{\frac{8}{9}} = x^{-7 + \frac{8}{9}} = x^{-6\frac{1}{9}}\)

\({\sqrt[6]{x^{5}} \over \sqrt[9]{x^{7}}} = {x^{\frac{5}{6}} \over x^{\frac{7}{9}}} = x^{\frac{5}{6} - \frac{7}{9}} = x^{\frac{1}{18}}\)

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

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

\({x^{9} \over x^{6} ⋅ \sqrt[4]{x^{3}}} = {x^{9} \over x^{6} ⋅ x^{\frac{3}{4}}} = {x^{9} \over x^{6\frac{3}{4}}} = x^{9 - 6\frac{3}{4}} = x^{2\frac{1}{4}}\)

\({4 y^{3} \over 7 x^{9}}\)

\((5 a)^{-2} = 5^{-2} ⋅ a^{-2} = {1 \over 5^{2}} ⋅ {1 \over a^{2}} = {1 \over 25 a^{2}}\)

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

\(2 p^{8\frac{2}{5}} = 2 ⋅ p^{8} ⋅ p^{\frac{2}{5}} = 2 p^{8} ⋅ \sqrt[5]{p^{2}}\)

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