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

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

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

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

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

\({({1 \over p^{9}}) \over p^{7}} = {p^{-9} \over p^{7}} = p^{-9 - 7} = p^{-16}\)

\({a^{7} \over a^{0}} = a^{7 - 0} = a^{7}\)

\({9 \over x^{7}}\)

\({8 p^{4} \over 9 p^{7}} = {8 \over 9} ⋅ {p^{4} \over p^{7}} = {8 \over 9} ⋅ p^{4 - 7} = {8 \over 9} p^{-3}\)

\({x^{4} \over ({1 \over x^{9}})} = {x^{4} \over x^{-9}} = x^{4 - -9} = x^{13}\)

\({8 a^{3} b \over 7 a b^{2}} = {8 \over 7} ⋅ {a^{3} \over a^{1}} ⋅ {b^{1} \over b^{2}} = {8 \over 7} ⋅ a^{3 - 1} ⋅ a^{1 - 2} = 1\frac{1}{7} a^{2} b^{-1}\)

\(a^{5} ⋅ \sqrt[3]{a} = a^{5} ⋅ a^{\frac{1}{3}} = a^{5 + \frac{1}{3}} = a^{5\frac{1}{3}}\)

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

\({p^{3} \over \sqrt[5]{p^{4}}} = {p^{3} \over p^{\frac{4}{5}}} = p^{3 - \frac{4}{5}} = p^{2\frac{1}{5}}\)

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

\({\sqrt[3]{a^{2}} \over \sqrt[7]{a^{3}}} = {a^{\frac{2}{3}} \over a^{\frac{3}{7}}} = a^{\frac{2}{3} - \frac{3}{7}} = a^{\frac{5}{21}}\)

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

\(\sqrt{x^{6}} = x^{\frac{6}{2}} = x^{3}\)

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

\({5 b^{5} \over 7 a^{4}}\)

\((2 a)^{-4} = 2^{-4} ⋅ a^{-4} = {1 \over 2^{4}} ⋅ {1 \over a^{4}} = {1 \over 16 a^{4}}\)

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

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

\(\frac{1}{7} a^{-\frac{5}{7}} b^{\frac{2}{7}} = \frac{1}{7} ⋅ {1 \over a^{\frac{5}{7}}} ⋅ b^{\frac{2}{7}} = {1 ⋅ \sqrt[7]{b^{2}} \over 7 ⋅ \sqrt[7]{a^{5}}}\)