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

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

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

\((x^{5})^{-9} = x^{5 ⋅ -9} = x^{-45}\)

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

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

\({x^{6} \over x^{0}} = x^{6 - 0} = x^{6}\)

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

\({7 a^{2} \over 8 a^{6}} = {7 \over 8} ⋅ {a^{2} \over a^{6}} = {7 \over 8} ⋅ a^{2 - 6} = {7 \over 8} a^{-4}\)

\({x^{3} \over ({1 \over x^{8}})} = {x^{3} \over x^{-8}} = x^{3 - -8} = x^{11}\)

\({8 a^{8} b^{4} \over 5 a^{5} b^{5}} = {8 \over 5} ⋅ {a^{8} \over a^{5}} ⋅ {b^{4} \over b^{5}} = {8 \over 5} ⋅ a^{8 - 5} ⋅ a^{4 - 5} = 1\frac{3}{5} a^{3} b^{-1}\)

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

\(a^{6} ⋅ \sqrt[4]{a^{3}} = a^{6} ⋅ a^{\frac{3}{4}} = a^{6 + \frac{3}{4}} = a^{6\frac{3}{4}}\)

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

\({1 \over p^{3}} ⋅ \sqrt[9]{p^{2}} = p^{-3} ⋅ p^{\frac{2}{9}} = p^{-3 + \frac{2}{9}} = p^{-2\frac{7}{9}}\)

\({\sqrt[7]{x^{3}} \over \sqrt[9]{x^{2}}} = {x^{\frac{3}{7}} \over x^{\frac{2}{9}}} = x^{\frac{3}{7} - \frac{2}{9}} = x^{\frac{13}{63}}\)

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

\(\sqrt[5]{x^{10}} = x^{\frac{10}{5}} = x^{2}\)

\({a^{2} \over a^{5} ⋅ \sqrt[9]{a^{7}}} = {a^{2} \over a^{5} ⋅ a^{\frac{7}{9}}} = {a^{2} \over a^{5\frac{7}{9}}} = a^{2 - 5\frac{7}{9}} = a^{-3\frac{7}{9}}\)

\({4 b^{8} \over 9 a^{4}}\)

\((2 p)^{-5} = 2^{-5} ⋅ p^{-5} = {1 \over 2^{5}} ⋅ {1 \over p^{5}} = {1 \over 32 p^{5}}\)

\(({1 \over 2} x)^{-3} = (2^{-1} ⋅ x)^{-3} = (2^{-1})^{-3} ⋅ x^{-3} = 2^{3} ⋅ x^{-3} = {8 \over x^{3}}\)

\(6 a^{5\frac{7}{9}} = 6 ⋅ a^{5} ⋅ a^{\frac{7}{9}} = 6 a^{5} ⋅ \sqrt[9]{a^{7}}\)

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