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

\({x^{2} \over x^{-4}} = x^{2 - -4} = x^{6}\)

\(p^{2} ⋅ p^{-7} = p^{2 + -7} = p^{-5}\)

\((x^{2})^{-5} = x^{2 ⋅ -5} = x^{-10}\)

\(a^{6} ⋅ {1 \over a^{7}} = a^{6} ⋅ a^{-7} = a^{6 + -7} = a^{-1}\)

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

\({p^{0} \over p^{3}} = p^{0 - 3} = p^{-3}\)

\({2 \over a^{3}}\)

\({5 a^{5} \over 9 a^{8}} = {5 \over 9} ⋅ {a^{5} \over a^{8}} = {5 \over 9} ⋅ a^{5 - 8} = {5 \over 9} a^{-3}\)

\({x^{2} \over ({1 \over x^{5}})} = {x^{2} \over x^{-5}} = x^{2 - -5} = x^{7}\)

\({7 p^{8} q \over 4 p^{3} q^{6}} = {7 \over 4} ⋅ {p^{8} \over p^{3}} ⋅ {q^{1} \over q^{6}} = {7 \over 4} ⋅ p^{8 - 3} ⋅ p^{1 - 6} = 1\frac{3}{4} p^{5} q^{-5}\)

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

\(x^{4} ⋅ \sqrt[7]{x^{3}} = x^{4} ⋅ x^{\frac{3}{7}} = x^{4 + \frac{3}{7}} = x^{4\frac{3}{7}}\)

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

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

\({\sqrt[6]{a^{5}} \over \sqrt[7]{a^{5}}} = {a^{\frac{5}{6}} \over a^{\frac{5}{7}}} = a^{\frac{5}{6} - \frac{5}{7}} = a^{\frac{5}{42}}\)

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

\(\sqrt[3]{a^{15}} = a^{\frac{15}{3}} = a^{5}\)

\({p^{6} \over p^{3} ⋅ \sqrt[8]{p^{5}}} = {p^{6} \over p^{3} ⋅ p^{\frac{5}{8}}} = {p^{6} \over p^{3\frac{5}{8}}} = p^{6 - 3\frac{5}{8}} = p^{2\frac{3}{8}}\)

\({3 y^{6} \over 7 x^{2}}\)

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

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

\(2 x^{7\frac{5}{6}} = 2 ⋅ x^{7} ⋅ x^{\frac{5}{6}} = 2 x^{7} ⋅ \sqrt[6]{x^{5}}\)

\(\frac{1}{5} p^{-\frac{3}{8}} q^{\frac{5}{8}} = \frac{1}{5} ⋅ {1 \over p^{\frac{3}{8}}} ⋅ q^{\frac{5}{8}} = {1 ⋅ \sqrt[8]{q^{5}} \over 5 ⋅ \sqrt[8]{p^{3}}}\)