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

\({3 x^{3} \over 5 x^{7}} = {3 \over 5} ⋅ {x^{3} \over x^{7}} = {3 \over 5} ⋅ x^{3 - 7} = {3 \over 5} x^{-4}\)

\({a^{4} \over a^{-7}} = a^{4 - -7} = a^{11}\)

\(p^{5} ⋅ p^{-9} = p^{5 + -9} = p^{-4}\)

\((a^{5})^{-8} = a^{5 ⋅ -8} = a^{-40}\)

\(x^{4} ⋅ {1 \over x^{5}} = x^{4} ⋅ x^{-5} = x^{4 + -5} = x^{-1}\)

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

\({a^{5} \over ({1 \over a^{7}})} = {a^{5} \over a^{-7}} = a^{5 - -7} = a^{12}\)

\({9 a^{8} b^{3} \over 7 a^{3} b^{6}} = {9 \over 7} ⋅ {a^{8} \over a^{3}} ⋅ {b^{3} \over b^{6}} = {9 \over 7} ⋅ a^{8 - 3} ⋅ a^{3 - 6} = 1\frac{2}{7} a^{5} b^{-3}\)

\({x^{0} \over x^{4}} = x^{0 - 4} = x^{-4}\)

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

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

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

\({1 \over a^{9}} ⋅ \sqrt[9]{a^{2}} = a^{-9} ⋅ a^{\frac{2}{9}} = a^{-9 + \frac{2}{9}} = a^{-8\frac{7}{9}}\)

\({\sqrt[4]{x^{3}} \over \sqrt[9]{x^{5}}} = {x^{\frac{3}{4}} \over x^{\frac{5}{9}}} = x^{\frac{3}{4} - \frac{5}{9}} = x^{\frac{7}{36}}\)

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

\(\sqrt[4]{p^{16}} = p^{\frac{16}{4}} = p^{4}\)

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

\({8 \over p^{5}}\)

\({3 b^{8} \over 4 a^{9}}\)

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

\(8 p^{7\frac{5}{6}} = 8 ⋅ p^{7} ⋅ p^{\frac{5}{6}} = 8 p^{7} ⋅ \sqrt[6]{p^{5}}\)

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

\((5 x)^{-2} = 5^{-2} ⋅ x^{-2} = {1 \over 5^{2}} ⋅ {1 \over x^{2}} = {1 \over 25 x^{2}}\)