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

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

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

\((a^{2})^{-3} = a^{2 ⋅ -3} = a^{-6}\)

\(x^{4} ⋅ {1 \over x^{8}} = x^{4} ⋅ x^{-8} = x^{4 + -8} = x^{-4}\)

\({({1 \over p^{5}}) \over p^{3}} = {p^{-5} \over p^{3}} = p^{-5 - 3} = p^{-8}\)

\({x^{0} \over x^{5}} = x^{0 - 5} = x^{-5}\)

\({7 \over x^{9}}\)

\({2 p^{4} \over 3 p^{6}} = {2 \over 3} ⋅ {p^{4} \over p^{6}} = {2 \over 3} ⋅ p^{4 - 6} = {2 \over 3} p^{-2}\)

\({x^{5} \over ({1 \over x^{7}})} = {x^{5} \over x^{-7}} = x^{5 - -7} = x^{12}\)

\({9 x^{8} y^{4} \over 2 x^{3} y^{6}} = {9 \over 2} ⋅ {x^{8} \over x^{3}} ⋅ {y^{4} \over y^{6}} = {9 \over 2} ⋅ x^{8 - 3} ⋅ x^{4 - 6} = 4\frac{1}{2} x^{5} y^{-2}\)

\(a^{6} ⋅ \sqrt[3]{a} = a^{6} ⋅ a^{\frac{1}{3}} = a^{6 + \frac{1}{3}} = a^{6\frac{1}{3}}\)

\(a^{6} ⋅ \sqrt[9]{a^{2}} = a^{6} ⋅ a^{\frac{2}{9}} = a^{6 + \frac{2}{9}} = a^{6\frac{2}{9}}\)

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

\({1 \over p^{7}} ⋅ \sqrt[9]{p^{4}} = p^{-7} ⋅ p^{\frac{4}{9}} = p^{-7 + \frac{4}{9}} = p^{-6\frac{5}{9}}\)

\({\sqrt[4]{x^{3}} \over \sqrt[7]{x^{3}}} = {x^{\frac{3}{4}} \over x^{\frac{3}{7}}} = x^{\frac{3}{4} - \frac{3}{7}} = x^{\frac{9}{28}}\)

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

\(\sqrt{a^{8}} = a^{\frac{8}{2}} = a^{4}\)

\({p^{2} \over p^{5} ⋅ \sqrt[3]{p^{2}}} = {p^{2} \over p^{5} ⋅ p^{\frac{2}{3}}} = {p^{2} \over p^{5\frac{2}{3}}} = p^{2 - 5\frac{2}{3}} = p^{-3\frac{2}{3}}\)

\({5 b^{8} \over 9 a^{3}}\)

\((3 a)^{-4} = 3^{-4} ⋅ a^{-4} = {1 \over 3^{4}} ⋅ {1 \over a^{4}} = {1 \over 81 a^{4}}\)

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

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

\(\frac{5}{6} x^{-\frac{1}{3}} y^{\frac{6}{7}} = \frac{5}{6} ⋅ {1 \over x^{\frac{1}{3}}} ⋅ y^{\frac{6}{7}} = {5 ⋅ \sqrt[7]{y^{6}} \over 6 ⋅ \sqrt[3]{x}}\)