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

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

\(x^{2} ⋅ x^{-9} = x^{2 + -9} = x^{-7}\)

\((a^{6})^{-3} = a^{6 ⋅ -3} = a^{-18}\)

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

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

\({a^{4} \over a^{0}} = a^{4 - 0} = a^{4}\)

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

\({3 a^{3} \over 8 a^{8}} = {3 \over 8} ⋅ {a^{3} \over a^{8}} = {3 \over 8} ⋅ a^{3 - 8} = {3 \over 8} a^{-5}\)

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

\({8 x^{6} y^{2} \over 7 x^{4} y^{3}} = {8 \over 7} ⋅ {x^{6} \over x^{4}} ⋅ {y^{2} \over y^{3}} = {8 \over 7} ⋅ x^{6 - 4} ⋅ x^{2 - 3} = 1\frac{1}{7} x^{2} y^{-1}\)

\(p^{7} ⋅ \sqrt[3]{p} = p^{7} ⋅ p^{\frac{1}{3}} = p^{7 + \frac{1}{3}} = p^{7\frac{1}{3}}\)

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

\({x^{2} \over \sqrt[8]{x^{3}}} = {x^{2} \over x^{\frac{3}{8}}} = x^{2 - \frac{3}{8}} = x^{1\frac{5}{8}}\)

\({1 \over a^{8}} ⋅ \sqrt[5]{a^{3}} = a^{-8} ⋅ a^{\frac{3}{5}} = a^{-8 + \frac{3}{5}} = a^{-7\frac{2}{5}}\)

\({\sqrt[7]{a^{6}} \over \sqrt[5]{a^{2}}} = {a^{\frac{6}{7}} \over a^{\frac{2}{5}}} = a^{\frac{6}{7} - \frac{2}{5}} = a^{\frac{16}{35}}\)

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

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

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

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

\((3 x)^{-4} = 3^{-4} ⋅ x^{-4} = {1 \over 3^{4}} ⋅ {1 \over x^{4}} = {1 \over 81 x^{4}}\)

\(({1 \over 3} x)^{-2} = (3^{-1} ⋅ x)^{-2} = (3^{-1})^{-2} ⋅ x^{-2} = 3^{2} ⋅ x^{-2} = {9 \over x^{2}}\)

\(8 a^{7\frac{3}{7}} = 8 ⋅ a^{7} ⋅ a^{\frac{3}{7}} = 8 a^{7} ⋅ \sqrt[7]{a^{3}}\)

\(\frac{4}{5} p^{-\frac{6}{7}} q^{\frac{3}{4}} = \frac{4}{5} ⋅ {1 \over p^{\frac{6}{7}}} ⋅ q^{\frac{3}{4}} = {4 ⋅ \sqrt[4]{q^{3}} \over 5 ⋅ \sqrt[7]{p^{6}}}\)