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

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

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

\((a^{2})^{-7} = a^{2 ⋅ -7} = a^{-14}\)

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

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

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

\({6 \over a^{4}}\)

\({4 a^{3} \over 9 a^{4}} = {4 \over 9} ⋅ {a^{3} \over a^{4}} = {4 \over 9} ⋅ a^{3 - 4} = {4 \over 9} a^{-1}\)

\({p^{4} \over ({1 \over p^{9}})} = {p^{4} \over p^{-9}} = p^{4 - -9} = p^{13}\)

\({9 a^{5} b^{3} \over 7 a^{3} b^{4}} = {9 \over 7} ⋅ {a^{5} \over a^{3}} ⋅ {b^{3} \over b^{4}} = {9 \over 7} ⋅ a^{5 - 3} ⋅ a^{3 - 4} = 1\frac{2}{7} a^{2} b^{-1}\)

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

\(p^{9} ⋅ \sqrt[7]{p^{6}} = p^{9} ⋅ p^{\frac{6}{7}} = p^{9 + \frac{6}{7}} = p^{9\frac{6}{7}}\)

\({a^{7} \over \sqrt[7]{a^{4}}} = {a^{7} \over a^{\frac{4}{7}}} = a^{7 - \frac{4}{7}} = a^{6\frac{3}{7}}\)

\({1 \over x^{8}} ⋅ \sqrt[6]{x^{5}} = x^{-8} ⋅ x^{\frac{5}{6}} = x^{-8 + \frac{5}{6}} = x^{-7\frac{1}{6}}\)

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

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

\(\sqrt[4]{a^{16}} = a^{\frac{16}{4}} = a^{4}\)

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

\({3 y^{9} \over 5 x^{4}}\)

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

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

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

\(\frac{7}{8} p^{-\frac{2}{3}} q^{\frac{6}{7}} = \frac{7}{8} ⋅ {1 \over p^{\frac{2}{3}}} ⋅ q^{\frac{6}{7}} = {7 ⋅ \sqrt[7]{q^{6}} \over 8 ⋅ \sqrt[3]{p^{2}}}\)