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

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

\({p^{3} \over p^{-7}} = p^{3 - -7} = p^{10}\)

\(a^{4} ⋅ a^{-9} = a^{4 + -9} = a^{-5}\)

\((a^{9})^{-8} = a^{9 ⋅ -8} = a^{-72}\)

\(a^{5} ⋅ {1 \over a^{9}} = a^{5} ⋅ a^{-9} = a^{5 + -9} = a^{-4}\)

\({({1 \over a^{8}}) \over a^{5}} = {a^{-8} \over a^{5}} = a^{-8 - 5} = a^{-13}\)

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

\({5 x^{4} y^{5} \over 4 x y^{10}} = {5 \over 4} ⋅ {x^{4} \over x^{1}} ⋅ {y^{5} \over y^{10}} = {5 \over 4} ⋅ x^{4 - 1} ⋅ x^{5 - 10} = 1\frac{1}{4} x^{3} y^{-5}\)

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

\(a^{2} ⋅ \sqrt[4]{a} = a^{2} ⋅ a^{\frac{1}{4}} = a^{2 + \frac{1}{4}} = a^{2\frac{1}{4}}\)

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

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

\({1 \over x^{9}} ⋅ \sqrt[9]{x^{7}} = x^{-9} ⋅ x^{\frac{7}{9}} = x^{-9 + \frac{7}{9}} = x^{-8\frac{2}{9}}\)

\({\sqrt[8]{a^{5}} \over \sqrt[7]{a^{3}}} = {a^{\frac{5}{8}} \over a^{\frac{3}{7}}} = a^{\frac{5}{8} - \frac{3}{7}} = a^{\frac{11}{56}}\)

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

\(\sqrt[4]{x^{8}} = x^{\frac{8}{4}} = x^{2}\)

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

\({7 \over x^{9}}\)

\({5 q^{4} \over 8 p^{7}}\)

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

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

\(5 a^{2\frac{3}{5}} = 5 ⋅ a^{2} ⋅ a^{\frac{3}{5}} = 5 a^{2} ⋅ \sqrt[5]{a^{3}}\)

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