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

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

\(x^{3} ⋅ x^{-8} = x^{3 + -8} = x^{-5}\)

\((a^{4})^{-9} = a^{4 ⋅ -9} = a^{-36}\)

\(a^{2} ⋅ {1 \over a^{5}} = a^{2} ⋅ a^{-5} = a^{2 + -5} = a^{-3}\)

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

\({x^{9} \over x^{0}} = x^{9 - 0} = x^{9}\)

\({8 \over p^{2}}\)

\({5 p \over 9 p^{3}} = {5 \over 9} ⋅ {p \over p^{3}} = {5 \over 9} ⋅ p^{1 - 3} = {5 \over 9} p^{-2}\)

\({x^{4} \over ({1 \over x^{6}})} = {x^{4} \over x^{-6}} = x^{4 - -6} = x^{10}\)

\({3 x^{6} y^{2} \over 2 x^{5} y^{4}} = {3 \over 2} ⋅ {x^{6} \over x^{5}} ⋅ {y^{2} \over y^{4}} = {3 \over 2} ⋅ x^{6 - 5} ⋅ x^{2 - 4} = 1\frac{1}{2} x y^{-2}\)

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

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

\({x^{8} \over \sqrt[8]{x^{3}}} = {x^{8} \over x^{\frac{3}{8}}} = x^{8 - \frac{3}{8}} = x^{7\frac{5}{8}}\)

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

\({\sqrt[8]{p^{5}} \over \sqrt[9]{p^{2}}} = {p^{\frac{5}{8}} \over p^{\frac{2}{9}}} = p^{\frac{5}{8} - \frac{2}{9}} = p^{\frac{29}{72}}\)

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

\(\sqrt[5]{x^{25}} = x^{\frac{25}{5}} = x^{5}\)

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

\({5 b^{4} \over 9 a^{9}}\)

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

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

\(4 a^{9\frac{5}{8}} = 4 ⋅ a^{9} ⋅ a^{\frac{5}{8}} = 4 a^{9} ⋅ \sqrt[8]{a^{5}}\)

\(\frac{1}{7} p^{-\frac{1}{8}} q^{\frac{3}{5}} = \frac{1}{7} ⋅ {1 \over p^{\frac{1}{8}}} ⋅ q^{\frac{3}{5}} = {1 ⋅ \sqrt[5]{q^{3}} \over 7 ⋅ \sqrt[8]{p}}\)