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

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

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

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

\(x^{3} ⋅ {1 \over x^{7}} = x^{3} ⋅ x^{-7} = x^{3 + -7} = x^{-4}\)

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

\({a^{0} \over a^{9}} = a^{0 - 9} = a^{-9}\)

\({3 \over x^{2}}\)

\({4 x^{2} \over 5 x^{5}} = {4 \over 5} ⋅ {x^{2} \over x^{5}} = {4 \over 5} ⋅ x^{2 - 5} = {4 \over 5} x^{-3}\)

\({x^{3} \over ({1 \over x^{7}})} = {x^{3} \over x^{-7}} = x^{3 - -7} = x^{10}\)

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

\(a^{6} ⋅ \sqrt[4]{a} = a^{6} ⋅ a^{\frac{1}{4}} = a^{6 + \frac{1}{4}} = a^{6\frac{1}{4}}\)

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

\({a^{4} \over \sqrt[8]{a^{3}}} = {a^{4} \over a^{\frac{3}{8}}} = a^{4 - \frac{3}{8}} = a^{3\frac{5}{8}}\)

\({1 \over x^{9}} ⋅ \sqrt[9]{x^{5}} = x^{-9} ⋅ x^{\frac{5}{9}} = x^{-9 + \frac{5}{9}} = x^{-8\frac{4}{9}}\)

\({\sqrt[7]{x^{6}} \over \sqrt[6]{x^{5}}} = {x^{\frac{6}{7}} \over x^{\frac{5}{6}}} = x^{\frac{6}{7} - \frac{5}{6}} = x^{\frac{1}{42}}\)

\(\sqrt[9]{{1 \over p^{7}}} = \sqrt[9]{p^{-7}} = p^{-\frac{7}{9}}\)

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

\({a^{4} \over a^{8} ⋅ \sqrt[3]{a^{2}}} = {a^{4} \over a^{8} ⋅ a^{\frac{2}{3}}} = {a^{4} \over a^{8\frac{2}{3}}} = a^{4 - 8\frac{2}{3}} = a^{-4\frac{2}{3}}\)

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

\((5 p)^{-3} = 5^{-3} ⋅ p^{-3} = {1 \over 5^{3}} ⋅ {1 \over p^{3}} = {1 \over 125 p^{3}}\)

\(({1 \over 5} a)^{-3} = (5^{-1} ⋅ a)^{-3} = (5^{-1})^{-3} ⋅ a^{-3} = 5^{3} ⋅ a^{-3} = {125 \over a^{3}}\)

\(9 a^{3\frac{3}{7}} = 9 ⋅ a^{3} ⋅ a^{\frac{3}{7}} = 9 a^{3} ⋅ \sqrt[7]{a^{3}}\)

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