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

\({6 p \over 7 p^{6}} = {6 \over 7} ⋅ {p \over p^{6}} = {6 \over 7} ⋅ p^{1 - 6} = {6 \over 7} p^{-5}\)

\({a^{8} \over a^{-4}} = a^{8 - -4} = a^{12}\)

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

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

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

\({({1 \over x^{6}}) \over x^{2}} = {x^{-6} \over x^{2}} = x^{-6 - 2} = x^{-8}\)

\({a^{4} \over ({1 \over a^{9}})} = {a^{4} \over a^{-9}} = a^{4 - -9} = a^{13}\)

\({5 a^{4} b^{4} \over 4 a^{3} b^{6}} = {5 \over 4} ⋅ {a^{4} \over a^{3}} ⋅ {b^{4} \over b^{6}} = {5 \over 4} ⋅ a^{4 - 3} ⋅ a^{4 - 6} = 1\frac{1}{4} a b^{-2}\)

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

\(p^{3} ⋅ \sqrt{p} = p^{3} ⋅ p^{\frac{1}{2}} = p^{3 + \frac{1}{2}} = p^{3\frac{1}{2}}\)

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

\({x^{6} \over \sqrt[8]{x^{3}}} = {x^{6} \over x^{\frac{3}{8}}} = x^{6 - \frac{3}{8}} = x^{5\frac{5}{8}}\)

\({1 \over p^{5}} ⋅ \sqrt[9]{p^{2}} = p^{-5} ⋅ p^{\frac{2}{9}} = p^{-5 + \frac{2}{9}} = p^{-4\frac{7}{9}}\)

\({\sqrt[8]{x^{5}} \over \sqrt[7]{x^{4}}} = {x^{\frac{5}{8}} \over x^{\frac{4}{7}}} = x^{\frac{5}{8} - \frac{4}{7}} = x^{\frac{3}{56}}\)

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

\(\sqrt[3]{a^{9}} = a^{\frac{9}{3}} = a^{3}\)

\({a^{8} \over a^{3} ⋅ \sqrt[9]{a^{2}}} = {a^{8} \over a^{3} ⋅ a^{\frac{2}{9}}} = {a^{8} \over a^{3\frac{2}{9}}} = a^{8 - 3\frac{2}{9}} = a^{4\frac{7}{9}}\)

\({8 \over a^{6}}\)

\({2 y^{2} \over 7 x^{4}}\)

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

\(4 a^{8\frac{2}{3}} = 4 ⋅ a^{8} ⋅ a^{\frac{2}{3}} = 4 a^{8} ⋅ \sqrt[3]{a^{2}}\)

\(\frac{5}{8} x^{-\frac{3}{7}} y^{\frac{1}{8}} = \frac{5}{8} ⋅ {1 \over x^{\frac{3}{7}}} ⋅ y^{\frac{1}{8}} = {5 ⋅ \sqrt[8]{y} \over 8 ⋅ \sqrt[7]{x^{3}}}\)

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