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

\({a^{9} \over a^{-5}} = a^{9 - -5} = a^{14}\)

\(x^{4} ⋅ x^{-6} = x^{4 + -6} = x^{-2}\)

\((a^{8})^{-7} = a^{8 ⋅ -7} = a^{-56}\)

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

\({({1 \over x^{9}}) \over x^{7}} = {x^{-9} \over x^{7}} = x^{-9 - 7} = x^{-16}\)

\({p^{7} \over p^{0}} = p^{7 - 0} = p^{7}\)

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

\({2 p^{2} \over 5 p^{5}} = {2 \over 5} ⋅ {p^{2} \over p^{5}} = {2 \over 5} ⋅ p^{2 - 5} = {2 \over 5} p^{-3}\)

\({a^{7} \over ({1 \over a^{8}})} = {a^{7} \over a^{-8}} = a^{7 - -8} = a^{15}\)

\({7 p^{6} q^{3} \over 2 p^{5} q^{8}} = {7 \over 2} ⋅ {p^{6} \over p^{5}} ⋅ {q^{3} \over q^{8}} = {7 \over 2} ⋅ p^{6 - 5} ⋅ p^{3 - 8} = 3\frac{1}{2} p q^{-5}\)

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

\(a^{9} ⋅ \sqrt[7]{a^{2}} = a^{9} ⋅ a^{\frac{2}{7}} = a^{9 + \frac{2}{7}} = a^{9\frac{2}{7}}\)

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

\({1 \over x^{5}} ⋅ \sqrt[9]{x^{8}} = x^{-5} ⋅ x^{\frac{8}{9}} = x^{-5 + \frac{8}{9}} = x^{-4\frac{1}{9}}\)

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

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

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

\({x^{4} \over x^{3} ⋅ \sqrt[9]{x^{2}}} = {x^{4} \over x^{3} ⋅ x^{\frac{2}{9}}} = {x^{4} \over x^{3\frac{2}{9}}} = x^{4 - 3\frac{2}{9}} = x^{\frac{7}{9}}\)

\({2 y^{2} \over 5 x^{5}}\)

\((3 a)^{-5} = 3^{-5} ⋅ a^{-5} = {1 \over 3^{5}} ⋅ {1 \over a^{5}} = {1 \over 243 a^{5}}\)

\(({1 \over 3} x)^{-5} = (3^{-1} ⋅ x)^{-5} = (3^{-1})^{-5} ⋅ x^{-5} = 3^{5} ⋅ x^{-5} = {243 \over x^{5}}\)

\(9 a^{3\frac{6}{7}} = 9 ⋅ a^{3} ⋅ a^{\frac{6}{7}} = 9 a^{3} ⋅ \sqrt[7]{a^{6}}\)

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