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

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

\(p^{2} ⋅ p^{-9} = p^{2 + -9} = p^{-7}\)

\((a^{7})^{-6} = a^{7 ⋅ -6} = a^{-42}\)

\(a^{3} ⋅ {1 \over a^{9}} = a^{3} ⋅ a^{-9} = a^{3 + -9} = a^{-6}\)

\({({1 \over p^{9}}) \over p^{2}} = {p^{-9} \over p^{2}} = p^{-9 - 2} = p^{-11}\)

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

\({2 \over a^{8}}\)

\({8 a^{5} \over 9 a^{10}} = {8 \over 9} ⋅ {a^{5} \over a^{10}} = {8 \over 9} ⋅ a^{5 - 10} = {8 \over 9} a^{-5}\)

\({a^{2} \over ({1 \over a^{5}})} = {a^{2} \over a^{-5}} = a^{2 - -5} = a^{7}\)

\({7 p^{5} q^{5} \over 4 p^{4} q^{10}} = {7 \over 4} ⋅ {p^{5} \over p^{4}} ⋅ {q^{5} \over q^{10}} = {7 \over 4} ⋅ p^{5 - 4} ⋅ p^{5 - 10} = 1\frac{3}{4} p q^{-5}\)

\(a^{4} ⋅ \sqrt{a} = a^{4} ⋅ a^{\frac{1}{2}} = a^{4 + \frac{1}{2}} = a^{4\frac{1}{2}}\)

\(a^{9} ⋅ \sqrt[5]{a^{4}} = a^{9} ⋅ a^{\frac{4}{5}} = a^{9 + \frac{4}{5}} = a^{9\frac{4}{5}}\)

\({x^{7} \over \sqrt[8]{x^{3}}} = {x^{7} \over x^{\frac{3}{8}}} = x^{7 - \frac{3}{8}} = x^{6\frac{5}{8}}\)

\({1 \over x^{6}} ⋅ \sqrt[4]{x^{3}} = x^{-6} ⋅ x^{\frac{3}{4}} = x^{-6 + \frac{3}{4}} = x^{-5\frac{1}{4}}\)

\({\sqrt[8]{a^{7}} \over \sqrt[5]{a^{2}}} = {a^{\frac{7}{8}} \over a^{\frac{2}{5}}} = a^{\frac{7}{8} - \frac{2}{5}} = a^{\frac{19}{40}}\)

\(\sqrt[7]{{1 \over p^{4}}} = \sqrt[7]{p^{-4}} = p^{-\frac{4}{7}}\)

\(\sqrt[5]{x^{10}} = x^{\frac{10}{5}} = x^{2}\)

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

\({7 y^{6} \over 8 x^{4}}\)

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

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

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

\(\frac{5}{6} x^{-\frac{2}{5}} y^{\frac{7}{8}} = \frac{5}{6} ⋅ {1 \over x^{\frac{2}{5}}} ⋅ y^{\frac{7}{8}} = {5 ⋅ \sqrt[8]{y^{7}} \over 6 ⋅ \sqrt[5]{x^{2}}}\)