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

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

\(a^{7} ⋅ a^{-8} = a^{7 + -8} = a^{-1}\)

\((p^{3})^{-9} = p^{3 ⋅ -9} = p^{-27}\)

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

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

\({x^{6} \over x^{0}} = x^{6 - 0} = x^{6}\)

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

\({2 x^{4} \over 7 x^{7}} = {2 \over 7} ⋅ {x^{4} \over x^{7}} = {2 \over 7} ⋅ x^{4 - 7} = {2 \over 7} x^{-3}\)

\({a^{8} \over ({1 \over a^{9}})} = {a^{8} \over a^{-9}} = a^{8 - -9} = a^{17}\)

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

\(a^{3} ⋅ \sqrt[8]{a} = a^{3} ⋅ a^{\frac{1}{8}} = a^{3 + \frac{1}{8}} = a^{3\frac{1}{8}}\)

\(x^{2} ⋅ \sqrt[7]{x^{6}} = x^{2} ⋅ x^{\frac{6}{7}} = x^{2 + \frac{6}{7}} = x^{2\frac{6}{7}}\)

\({p^{2} \over \sqrt[7]{p^{3}}} = {p^{2} \over p^{\frac{3}{7}}} = p^{2 - \frac{3}{7}} = p^{1\frac{4}{7}}\)

\({1 \over a^{7}} ⋅ \sqrt[4]{a^{3}} = a^{-7} ⋅ a^{\frac{3}{4}} = a^{-7 + \frac{3}{4}} = a^{-6\frac{1}{4}}\)

\({\sqrt[8]{a^{7}} \over \sqrt[7]{a^{5}}} = {a^{\frac{7}{8}} \over a^{\frac{5}{7}}} = a^{\frac{7}{8} - \frac{5}{7}} = a^{\frac{9}{56}}\)

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

\(\sqrt[3]{p^{12}} = p^{\frac{12}{3}} = p^{4}\)

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

\({3 q^{6} \over 7 p^{8}}\)

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

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

\(4 x^{3\frac{3}{8}} = 4 ⋅ x^{3} ⋅ x^{\frac{3}{8}} = 4 x^{3} ⋅ \sqrt[8]{x^{3}}\)

\(\frac{2}{7} a^{-\frac{4}{9}} b^{\frac{4}{5}} = \frac{2}{7} ⋅ {1 \over a^{\frac{4}{9}}} ⋅ b^{\frac{4}{5}} = {2 ⋅ \sqrt[5]{b^{4}} \over 7 ⋅ \sqrt[9]{a^{4}}}\)