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

\({x^{8} \over x^{-2}} = x^{8 - -2} = x^{10}\)

\(p^{3} ⋅ p^{-4} = p^{3 + -4} = p^{-1}\)

\((x^{8})^{-4} = x^{8 ⋅ -4} = x^{-32}\)

\(a^{5} ⋅ {1 \over a^{7}} = a^{5} ⋅ a^{-7} = a^{5 + -7} = a^{-2}\)

\({({1 \over p^{8}}) \over p^{2}} = {p^{-8} \over p^{2}} = p^{-8 - 2} = p^{-10}\)

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

\({5 \over a^{9}}\)

\({8 a^{5} \over 9 a^{6}} = {8 \over 9} ⋅ {a^{5} \over a^{6}} = {8 \over 9} ⋅ a^{5 - 6} = {8 \over 9} a^{-1}\)

\({p^{6} \over ({1 \over p^{8}})} = {p^{6} \over p^{-8}} = p^{6 - -8} = p^{14}\)

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

\(x^{3} ⋅ \sqrt[9]{x} = x^{3} ⋅ x^{\frac{1}{9}} = x^{3 + \frac{1}{9}} = x^{3\frac{1}{9}}\)

\(a^{6} ⋅ \sqrt[3]{a^{2}} = a^{6} ⋅ a^{\frac{2}{3}} = a^{6 + \frac{2}{3}} = a^{6\frac{2}{3}}\)

\({x^{3} \over \sqrt[7]{x^{2}}} = {x^{3} \over x^{\frac{2}{7}}} = x^{3 - \frac{2}{7}} = x^{2\frac{5}{7}}\)

\({1 \over a^{2}} ⋅ \sqrt[3]{a^{2}} = a^{-2} ⋅ a^{\frac{2}{3}} = a^{-2 + \frac{2}{3}} = a^{-1\frac{1}{3}}\)

\({\sqrt[4]{p^{3}} \over \sqrt[3]{p^{2}}} = {p^{\frac{3}{4}} \over p^{\frac{2}{3}}} = p^{\frac{3}{4} - \frac{2}{3}} = p^{\frac{1}{12}}\)

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

\(\sqrt[4]{a^{20}} = a^{\frac{20}{4}} = a^{5}\)

\({x^{5} \over x^{6} ⋅ \sqrt[7]{x^{6}}} = {x^{5} \over x^{6} ⋅ x^{\frac{6}{7}}} = {x^{5} \over x^{6\frac{6}{7}}} = x^{5 - 6\frac{6}{7}} = x^{-1\frac{6}{7}}\)

\({3 y^{9} \over 8 x^{8}}\)

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

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

\(4 a^{2\frac{7}{8}} = 4 ⋅ a^{2} ⋅ a^{\frac{7}{8}} = 4 a^{2} ⋅ \sqrt[8]{a^{7}}\)

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