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

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

\(a^{2} ⋅ a^{-7} = a^{2 + -7} = a^{-5}\)

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

\(p^{4} ⋅ {1 \over p^{6}} = p^{4} ⋅ p^{-6} = p^{4 + -6} = p^{-2}\)

\({({1 \over a^{9}}) \over a^{5}} = {a^{-9} \over a^{5}} = a^{-9 - 5} = a^{-14}\)

\({x^{3} \over x^{0}} = x^{3 - 0} = x^{3}\)

\({9 \over x^{5}}\)

\({7 p \over 9 p^{2}} = {7 \over 9} ⋅ {p \over p^{2}} = {7 \over 9} ⋅ p^{1 - 2} = {7 \over 9} p^{-1}\)

\({x^{4} \over ({1 \over x^{8}})} = {x^{4} \over x^{-8}} = x^{4 - -8} = x^{12}\)

\({6 p^{6} q \over 5 p^{2} q^{2}} = {6 \over 5} ⋅ {p^{6} \over p^{2}} ⋅ {q^{1} \over q^{2}} = {6 \over 5} ⋅ p^{6 - 2} ⋅ p^{1 - 2} = 1\frac{1}{5} p^{4} q^{-1}\)

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

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

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

\({1 \over x^{2}} ⋅ \sqrt[5]{x^{4}} = x^{-2} ⋅ x^{\frac{4}{5}} = x^{-2 + \frac{4}{5}} = x^{-1\frac{1}{5}}\)

\({\sqrt[9]{x^{8}} \over \sqrt[8]{x^{3}}} = {x^{\frac{8}{9}} \over x^{\frac{3}{8}}} = x^{\frac{8}{9} - \frac{3}{8}} = x^{\frac{37}{72}}\)

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

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

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

\({7 b^{3} \over 8 a^{4}}\)

\((3 x)^{-5} = 3^{-5} ⋅ x^{-5} = {1 \over 3^{5}} ⋅ {1 \over x^{5}} = {1 \over 243 x^{5}}\)

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

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

\(\frac{7}{9} x^{-\frac{5}{8}} y^{\frac{3}{4}} = \frac{7}{9} ⋅ {1 \over x^{\frac{5}{8}}} ⋅ y^{\frac{3}{4}} = {7 ⋅ \sqrt[4]{y^{3}} \over 9 ⋅ \sqrt[8]{x^{5}}}\)