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

\({p^{5} \over p^{-8}} = p^{5 - -8} = p^{13}\)

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

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

\(a^{5} ⋅ {1 \over a^{8}} = a^{5} ⋅ a^{-8} = a^{5 + -8} = a^{-3}\)

\({({1 \over a^{6}}) \over a^{3}} = {a^{-6} \over a^{3}} = a^{-6 - 3} = a^{-9}\)

\({a^{8} \over a^{0}} = a^{8 - 0} = a^{8}\)

\({6 \over p^{2}}\)

\({3 x^{2} \over 5 x^{4}} = {3 \over 5} ⋅ {x^{2} \over x^{4}} = {3 \over 5} ⋅ x^{2 - 4} = {3 \over 5} x^{-2}\)

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

\({7 a^{7} b \over 3 a^{5} b^{5}} = {7 \over 3} ⋅ {a^{7} \over a^{5}} ⋅ {b^{1} \over b^{5}} = {7 \over 3} ⋅ a^{7 - 5} ⋅ a^{1 - 5} = 2\frac{1}{3} a^{2} b^{-4}\)

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

\(p^{4} ⋅ \sqrt[5]{p^{4}} = p^{4} ⋅ p^{\frac{4}{5}} = p^{4 + \frac{4}{5}} = p^{4\frac{4}{5}}\)

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

\({1 \over x^{9}} ⋅ \sqrt[7]{x^{6}} = x^{-9} ⋅ x^{\frac{6}{7}} = x^{-9 + \frac{6}{7}} = x^{-8\frac{1}{7}}\)

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

\(\sqrt[9]{{1 \over x^{5}}} = \sqrt[9]{x^{-5}} = x^{-\frac{5}{9}}\)

\(\sqrt{x^{10}} = x^{\frac{10}{2}} = x^{5}\)

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

\({5 y^{9} \over 8 x^{6}}\)

\((4 p)^{-3} = 4^{-3} ⋅ p^{-3} = {1 \over 4^{3}} ⋅ {1 \over p^{3}} = {1 \over 64 p^{3}}\)

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

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

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