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

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

\(x^{7} ⋅ x^{-9} = x^{7 + -9} = x^{-2}\)

\((x^{8})^{-2} = x^{8 ⋅ -2} = x^{-16}\)

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

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

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

\({4 \over p^{5}}\)

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

\({x^{4} \over ({1 \over x^{7}})} = {x^{4} \over x^{-7}} = x^{4 - -7} = x^{11}\)

\({9 p^{10} q^{4} \over 7 p^{5} q^{5}} = {9 \over 7} ⋅ {p^{10} \over p^{5}} ⋅ {q^{4} \over q^{5}} = {9 \over 7} ⋅ p^{10 - 5} ⋅ p^{4 - 5} = 1\frac{2}{7} p^{5} q^{-1}\)

\(a^{8} ⋅ \sqrt[9]{a} = a^{8} ⋅ a^{\frac{1}{9}} = a^{8 + \frac{1}{9}} = a^{8\frac{1}{9}}\)

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

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

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

\({\sqrt[9]{a^{7}} \over \sqrt[4]{a^{3}}} = {a^{\frac{7}{9}} \over a^{\frac{3}{4}}} = a^{\frac{7}{9} - \frac{3}{4}} = a^{\frac{1}{36}}\)

\(\sqrt[5]{{1 \over x^{3}}} = \sqrt[5]{x^{-3}} = x^{-\frac{3}{5}}\)

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

\({x^{9} \over x^{2} ⋅ \sqrt[6]{x^{5}}} = {x^{9} \over x^{2} ⋅ x^{\frac{5}{6}}} = {x^{9} \over x^{2\frac{5}{6}}} = x^{9 - 2\frac{5}{6}} = x^{6\frac{1}{6}}\)

\({4 b^{9} \over 9 a^{7}}\)

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

\(({1 \over 3} x)^{-4} = (3^{-1} ⋅ x)^{-4} = (3^{-1})^{-4} ⋅ x^{-4} = 3^{4} ⋅ x^{-4} = {81 \over x^{4}}\)

\(8 p^{7\frac{6}{7}} = 8 ⋅ p^{7} ⋅ p^{\frac{6}{7}} = 8 p^{7} ⋅ \sqrt[7]{p^{6}}\)

\(\frac{3}{4} a^{-\frac{5}{8}} b^{\frac{3}{5}} = \frac{3}{4} ⋅ {1 \over a^{\frac{5}{8}}} ⋅ b^{\frac{3}{5}} = {3 ⋅ \sqrt[5]{b^{3}} \over 4 ⋅ \sqrt[8]{a^{5}}}\)