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

\({a^{7} \over a^{-8}} = a^{7 - -8} = a^{15}\)

\(p^{5} ⋅ p^{-6} = p^{5 + -6} = p^{-1}\)

\((a^{7})^{-5} = a^{7 ⋅ -5} = a^{-35}\)

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

\({({1 \over p^{7}}) \over p^{4}} = {p^{-7} \over p^{4}} = p^{-7 - 4} = p^{-11}\)

\({x^{0} \over x^{4}} = x^{0 - 4} = x^{-4}\)

\({2 \over x^{9}}\)

\({2 p^{3} \over 9 p^{5}} = {2 \over 9} ⋅ {p^{3} \over p^{5}} = {2 \over 9} ⋅ p^{3 - 5} = {2 \over 9} p^{-2}\)

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

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

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

\(p^{8} ⋅ \sqrt[8]{p^{7}} = p^{8} ⋅ p^{\frac{7}{8}} = p^{8 + \frac{7}{8}} = p^{8\frac{7}{8}}\)

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

\({1 \over a^{2}} ⋅ \sqrt[9]{a^{7}} = a^{-2} ⋅ a^{\frac{7}{9}} = a^{-2 + \frac{7}{9}} = a^{-1\frac{2}{9}}\)

\({\sqrt[3]{a^{2}} \over \sqrt[9]{a^{4}}} = {a^{\frac{2}{3}} \over a^{\frac{4}{9}}} = a^{\frac{2}{3} - \frac{4}{9}} = a^{\frac{2}{9}}\)

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

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

\({p^{5} \over p^{3} ⋅ \sqrt[9]{p^{8}}} = {p^{5} \over p^{3} ⋅ p^{\frac{8}{9}}} = {p^{5} \over p^{3\frac{8}{9}}} = p^{5 - 3\frac{8}{9}} = p^{1\frac{1}{9}}\)

\({5 b^{9} \over 9 a^{4}}\)

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

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

\(9 a^{4\frac{4}{9}} = 9 ⋅ a^{4} ⋅ a^{\frac{4}{9}} = 9 a^{4} ⋅ \sqrt[9]{a^{4}}\)

\(\frac{7}{8} x^{-\frac{4}{9}} y^{\frac{5}{7}} = \frac{7}{8} ⋅ {1 \over x^{\frac{4}{9}}} ⋅ y^{\frac{5}{7}} = {7 ⋅ \sqrt[7]{y^{5}} \over 8 ⋅ \sqrt[9]{x^{4}}}\)