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

\({p^{7} \over p^{-5}} = p^{7 - -5} = p^{12}\)

\(x^{2} ⋅ x^{-4} = x^{2 + -4} = x^{-2}\)

\((a^{5})^{-7} = a^{5 ⋅ -7} = a^{-35}\)

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

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

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

\({3 \over x^{8}}\)

\({5 x^{4} \over 8 x^{6}} = {5 \over 8} ⋅ {x^{4} \over x^{6}} = {5 \over 8} ⋅ x^{4 - 6} = {5 \over 8} x^{-2}\)

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

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

\(a^{9} ⋅ \sqrt[5]{a} = a^{9} ⋅ a^{\frac{1}{5}} = a^{9 + \frac{1}{5}} = a^{9\frac{1}{5}}\)

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

\({x^{5} \over \sqrt[9]{x^{2}}} = {x^{5} \over x^{\frac{2}{9}}} = x^{5 - \frac{2}{9}} = x^{4\frac{7}{9}}\)

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

\({\sqrt[3]{x^{2}} \over \sqrt[8]{x^{5}}} = {x^{\frac{2}{3}} \over x^{\frac{5}{8}}} = x^{\frac{2}{3} - \frac{5}{8}} = x^{\frac{1}{24}}\)

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

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

\({x^{9} \over x^{6} ⋅ \sqrt[8]{x^{3}}} = {x^{9} \over x^{6} ⋅ x^{\frac{3}{8}}} = {x^{9} \over x^{6\frac{3}{8}}} = x^{9 - 6\frac{3}{8}} = x^{2\frac{5}{8}}\)

\({3 b^{6} \over 7 a^{5}}\)

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

\(({1 \over 4} a)^{-2} = (4^{-1} ⋅ a)^{-2} = (4^{-1})^{-2} ⋅ a^{-2} = 4^{2} ⋅ a^{-2} = {16 \over a^{2}}\)

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

\(\frac{4}{5} x^{-\frac{7}{9}} y^{\frac{5}{9}} = \frac{4}{5} ⋅ {1 \over x^{\frac{7}{9}}} ⋅ y^{\frac{5}{9}} = {4 ⋅ \sqrt[9]{y^{5}} \over 5 ⋅ \sqrt[9]{x^{7}}}\)