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

\({a^{5} \over a^{-8}} = a^{5 - -8} = a^{13}\)

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

\((x^{9})^{-7} = x^{9 ⋅ -7} = x^{-63}\)

\(a^{6} ⋅ {1 \over a^{9}} = a^{6} ⋅ a^{-9} = a^{6 + -9} = a^{-3}\)

\({({1 \over x^{7}}) \over x^{6}} = {x^{-7} \over x^{6}} = x^{-7 - 6} = x^{-13}\)

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

\({2 \over x^{6}}\)

\({4 a^{2} \over 5 a^{4}} = {4 \over 5} ⋅ {a^{2} \over a^{4}} = {4 \over 5} ⋅ a^{2 - 4} = {4 \over 5} a^{-2}\)

\({a^{4} \over ({1 \over a^{6}})} = {a^{4} \over a^{-6}} = a^{4 - -6} = a^{10}\)

\({9 x^{6} y^{3} \over 2 x y^{8}} = {9 \over 2} ⋅ {x^{6} \over x^{1}} ⋅ {y^{3} \over y^{8}} = {9 \over 2} ⋅ x^{6 - 1} ⋅ x^{3 - 8} = 4\frac{1}{2} x^{5} y^{-5}\)

\(x^{3} ⋅ \sqrt[4]{x} = x^{3} ⋅ x^{\frac{1}{4}} = x^{3 + \frac{1}{4}} = x^{3\frac{1}{4}}\)

\(a^{5} ⋅ \sqrt[7]{a^{5}} = a^{5} ⋅ a^{\frac{5}{7}} = a^{5 + \frac{5}{7}} = a^{5\frac{5}{7}}\)

\({p^{4} \over \sqrt[8]{p^{7}}} = {p^{4} \over p^{\frac{7}{8}}} = p^{4 - \frac{7}{8}} = p^{3\frac{1}{8}}\)

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

\({\sqrt[9]{x^{8}} \over \sqrt[7]{x^{3}}} = {x^{\frac{8}{9}} \over x^{\frac{3}{7}}} = x^{\frac{8}{9} - \frac{3}{7}} = x^{\frac{29}{63}}\)

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

\(\sqrt[5]{a^{15}} = a^{\frac{15}{5}} = a^{3}\)

\({p^{5} \over p^{6} ⋅ \sqrt[9]{p^{4}}} = {p^{5} \over p^{6} ⋅ p^{\frac{4}{9}}} = {p^{5} \over p^{6\frac{4}{9}}} = p^{5 - 6\frac{4}{9}} = p^{-1\frac{4}{9}}\)

\({8 y^{5} \over 9 x^{8}}\)

\((5 x)^{-4} = 5^{-4} ⋅ x^{-4} = {1 \over 5^{4}} ⋅ {1 \over x^{4}} = {1 \over 625 x^{4}}\)

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

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

\(\frac{2}{5} x^{-\frac{4}{9}} y^{\frac{1}{4}} = \frac{2}{5} ⋅ {1 \over x^{\frac{4}{9}}} ⋅ y^{\frac{1}{4}} = {2 ⋅ \sqrt[4]{y} \over 5 ⋅ \sqrt[9]{x^{4}}}\)