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

\({x^{7} \over x^{-9}} = x^{7 - -9} = x^{16}\)

\(p^{2} ⋅ p^{-3} = p^{2 + -3} = p^{-1}\)

\((a^{2})^{-4} = a^{2 ⋅ -4} = a^{-8}\)

\(a^{7} ⋅ {1 \over a^{8}} = a^{7} ⋅ a^{-8} = a^{7 + -8} = a^{-1}\)

\({({1 \over x^{9}}) \over x^{6}} = {x^{-9} \over x^{6}} = x^{-9 - 6} = x^{-15}\)

\({a^{0} \over a^{2}} = a^{0 - 2} = a^{-2}\)

\({7 \over a^{2}}\)

\({3 p^{2} \over 7 p^{6}} = {3 \over 7} ⋅ {p^{2} \over p^{6}} = {3 \over 7} ⋅ p^{2 - 6} = {3 \over 7} p^{-4}\)

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

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

\(a^{3} ⋅ \sqrt[5]{a} = a^{3} ⋅ a^{\frac{1}{5}} = a^{3 + \frac{1}{5}} = a^{3\frac{1}{5}}\)

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

\({a^{6} \over \sqrt[9]{a^{2}}} = {a^{6} \over a^{\frac{2}{9}}} = a^{6 - \frac{2}{9}} = a^{5\frac{7}{9}}\)

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

\({\sqrt[7]{x^{5}} \over \sqrt[8]{x^{3}}} = {x^{\frac{5}{7}} \over x^{\frac{3}{8}}} = x^{\frac{5}{7} - \frac{3}{8}} = x^{\frac{19}{56}}\)

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

\(\sqrt[3]{p^{12}} = p^{\frac{12}{3}} = p^{4}\)

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

\({5 b^{6} \over 9 a^{8}}\)

\((5 x)^{-4} = 5^{-4} ⋅ x^{-4} = {1 \over 5^{4}} ⋅ {1 \over x^{4}} = {1 \over 625 x^{4}}\)

\(({1 \over 2} a)^{-5} = (2^{-1} ⋅ a)^{-5} = (2^{-1})^{-5} ⋅ a^{-5} = 2^{5} ⋅ a^{-5} = {32 \over a^{5}}\)

\(8 x^{4\frac{7}{8}} = 8 ⋅ x^{4} ⋅ x^{\frac{7}{8}} = 8 x^{4} ⋅ \sqrt[8]{x^{7}}\)

\(\frac{4}{5} p^{-\frac{2}{3}} q^{\frac{1}{8}} = \frac{4}{5} ⋅ {1 \over p^{\frac{2}{3}}} ⋅ q^{\frac{1}{8}} = {4 ⋅ \sqrt[8]{q} \over 5 ⋅ \sqrt[3]{p^{2}}}\)