\({1 \over a^{4}} = a^{-4}\)

\({x^{9} \over x^{-2}} = x^{9 - -2} = x^{11}\)

\(a^{3} ⋅ a^{-9} = a^{3 + -9} = a^{-6}\)

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

\(p^{3} ⋅ {1 \over p^{7}} = p^{3} ⋅ p^{-7} = p^{3 + -7} = p^{-4}\)

\({({1 \over p^{8}}) \over p^{3}} = {p^{-8} \over p^{3}} = p^{-8 - 3} = p^{-11}\)

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

\({7 \over a^{5}}\)

\({3 x^{5} \over 8 x^{6}} = {3 \over 8} ⋅ {x^{5} \over x^{6}} = {3 \over 8} ⋅ x^{5 - 6} = {3 \over 8} x^{-1}\)

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

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

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

\(a^{9} ⋅ \sqrt[7]{a^{4}} = a^{9} ⋅ a^{\frac{4}{7}} = a^{9 + \frac{4}{7}} = a^{9\frac{4}{7}}\)

\({a^{3} \over \sqrt[9]{a^{5}}} = {a^{3} \over a^{\frac{5}{9}}} = a^{3 - \frac{5}{9}} = a^{2\frac{4}{9}}\)

\({1 \over x^{7}} ⋅ \sqrt[5]{x^{4}} = x^{-7} ⋅ x^{\frac{4}{5}} = x^{-7 + \frac{4}{5}} = x^{-6\frac{1}{5}}\)

\({\sqrt[7]{x^{4}} \over \sqrt[5]{x^{2}}} = {x^{\frac{4}{7}} \over x^{\frac{2}{5}}} = x^{\frac{4}{7} - \frac{2}{5}} = x^{\frac{6}{35}}\)

\(\sqrt[9]{{1 \over p^{2}}} = \sqrt[9]{p^{-2}} = p^{-\frac{2}{9}}\)

\(\sqrt[5]{a^{10}} = a^{\frac{10}{5}} = a^{2}\)

\({x^{8} \over x^{2} ⋅ \sqrt[5]{x^{4}}} = {x^{8} \over x^{2} ⋅ x^{\frac{4}{5}}} = {x^{8} \over x^{2\frac{4}{5}}} = x^{8 - 2\frac{4}{5}} = x^{5\frac{1}{5}}\)

\({6 b^{2} \over 7 a^{8}}\)

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

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

\(4 a^{3\frac{4}{9}} = 4 ⋅ a^{3} ⋅ a^{\frac{4}{9}} = 4 a^{3} ⋅ \sqrt[9]{a^{4}}\)

\(\frac{1}{2} x^{-\frac{1}{7}} y^{\frac{1}{9}} = \frac{1}{2} ⋅ {1 \over x^{\frac{1}{7}}} ⋅ y^{\frac{1}{9}} = {1 ⋅ \sqrt[9]{y} \over 2 ⋅ \sqrt[7]{x}}\)