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

\({p^{6} \over p^{-9}} = p^{6 - -9} = p^{15}\)

\(a^{2} ⋅ a^{-5} = a^{2 + -5} = a^{-3}\)

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

\(a^{6} ⋅ {1 \over a^{8}} = a^{6} ⋅ a^{-8} = a^{6 + -8} = a^{-2}\)

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

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

\({4 \over x^{9}}\)

\({7 x^{2} \over 9 x^{7}} = {7 \over 9} ⋅ {x^{2} \over x^{7}} = {7 \over 9} ⋅ x^{2 - 7} = {7 \over 9} x^{-5}\)

\({x^{2} \over ({1 \over x^{3}})} = {x^{2} \over x^{-3}} = x^{2 - -3} = x^{5}\)

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

\(x^{3} ⋅ \sqrt[7]{x} = x^{3} ⋅ x^{\frac{1}{7}} = x^{3 + \frac{1}{7}} = x^{3\frac{1}{7}}\)

\(a^{3} ⋅ \sqrt[8]{a^{3}} = a^{3} ⋅ a^{\frac{3}{8}} = a^{3 + \frac{3}{8}} = a^{3\frac{3}{8}}\)

\({p^{4} \over \sqrt[7]{p^{2}}} = {p^{4} \over p^{\frac{2}{7}}} = p^{4 - \frac{2}{7}} = p^{3\frac{5}{7}}\)

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

\({\sqrt[7]{p^{6}} \over \sqrt[3]{p^{2}}} = {p^{\frac{6}{7}} \over p^{\frac{2}{3}}} = p^{\frac{6}{7} - \frac{2}{3}} = p^{\frac{4}{21}}\)

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

\(\sqrt[5]{a^{20}} = a^{\frac{20}{5}} = a^{4}\)

\({x^{4} \over x^{7} ⋅ \sqrt[6]{x^{5}}} = {x^{4} \over x^{7} ⋅ x^{\frac{5}{6}}} = {x^{4} \over x^{7\frac{5}{6}}} = x^{4 - 7\frac{5}{6}} = x^{-3\frac{5}{6}}\)

\({7 b^{5} \over 8 a^{3}}\)

\((4 a)^{-5} = 4^{-5} ⋅ a^{-5} = {1 \over 4^{5}} ⋅ {1 \over a^{5}} = {1 \over 1\,024 a^{5}}\)

\(({1 \over 2} p)^{-3} = (2^{-1} ⋅ p)^{-3} = (2^{-1})^{-3} ⋅ p^{-3} = 2^{3} ⋅ p^{-3} = {8 \over p^{3}}\)

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

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