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

\({7 p^{4} \over 8 p^{9}} = {7 \over 8} ⋅ {p^{4} \over p^{9}} = {7 \over 8} ⋅ p^{4 - 9} = {7 \over 8} p^{-5}\)

\({x^{6} \over x^{-8}} = x^{6 - -8} = x^{14}\)

\(a^{2} ⋅ a^{-5} = a^{2 + -5} = a^{-3}\)

\((a^{4})^{-6} = a^{4 ⋅ -6} = a^{-24}\)

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

\({({1 \over x^{9}}) \over x^{3}} = {x^{-9} \over x^{3}} = x^{-9 - 3} = x^{-12}\)

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

\({7 x^{4} y^{2} \over 4 x y^{5}} = {7 \over 4} ⋅ {x^{4} \over x^{1}} ⋅ {y^{2} \over y^{5}} = {7 \over 4} ⋅ x^{4 - 1} ⋅ x^{2 - 5} = 1\frac{3}{4} x^{3} y^{-3}\)

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

\(p^{4} ⋅ \sqrt[7]{p} = p^{4} ⋅ p^{\frac{1}{7}} = p^{4 + \frac{1}{7}} = p^{4\frac{1}{7}}\)

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

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

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

\({\sqrt[8]{x^{7}} \over \sqrt[5]{x^{3}}} = {x^{\frac{7}{8}} \over x^{\frac{3}{5}}} = x^{\frac{7}{8} - \frac{3}{5}} = x^{\frac{11}{40}}\)

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

\(\sqrt[5]{p^{25}} = p^{\frac{25}{5}} = p^{5}\)

\({x^{4} \over x^{2} ⋅ \sqrt[9]{x^{7}}} = {x^{4} \over x^{2} ⋅ x^{\frac{7}{9}}} = {x^{4} \over x^{2\frac{7}{9}}} = x^{4 - 2\frac{7}{9}} = x^{1\frac{2}{9}}\)

\({3 \over p^{5}}\)

\({5 b^{7} \over 8 a^{4}}\)

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

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

\(2 a^{4\frac{5}{8}} = 2 ⋅ a^{4} ⋅ a^{\frac{5}{8}} = 2 a^{4} ⋅ \sqrt[8]{a^{5}}\)

\(\frac{1}{8} x^{-\frac{4}{9}} y^{\frac{7}{9}} = \frac{1}{8} ⋅ {1 \over x^{\frac{4}{9}}} ⋅ y^{\frac{7}{9}} = {1 ⋅ \sqrt[9]{y^{7}} \over 8 ⋅ \sqrt[9]{x^{4}}}\)