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

\({a^{3} \over a^{-2}} = a^{3 - -2} = a^{5}\)

\(x^{6} ⋅ x^{-8} = x^{6 + -8} = x^{-2}\)

\((a^{2})^{-7} = a^{2 ⋅ -7} = a^{-14}\)

\(x^{6} ⋅ {1 \over x^{7}} = x^{6} ⋅ x^{-7} = x^{6 + -7} = x^{-1}\)

\({({1 \over p^{3}}) \over p^{2}} = {p^{-3} \over p^{2}} = p^{-3 - 2} = p^{-5}\)

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

\({7 \over x^{6}}\)

\({7 a^{2} \over 9 a^{3}} = {7 \over 9} ⋅ {a^{2} \over a^{3}} = {7 \over 9} ⋅ a^{2 - 3} = {7 \over 9} a^{-1}\)

\({x^{6} \over ({1 \over x^{9}})} = {x^{6} \over x^{-9}} = x^{6 - -9} = x^{15}\)

\({9 x^{7} y^{3} \over 8 x^{4} y^{7}} = {9 \over 8} ⋅ {x^{7} \over x^{4}} ⋅ {y^{3} \over y^{7}} = {9 \over 8} ⋅ x^{7 - 4} ⋅ x^{3 - 7} = 1\frac{1}{8} x^{3} y^{-4}\)

\(a^{8} ⋅ \sqrt{a} = a^{8} ⋅ a^{\frac{1}{2}} = a^{8 + \frac{1}{2}} = a^{8\frac{1}{2}}\)

\(x^{5} ⋅ \sqrt[8]{x^{7}} = x^{5} ⋅ x^{\frac{7}{8}} = x^{5 + \frac{7}{8}} = x^{5\frac{7}{8}}\)

\({p^{9} \over \sqrt[7]{p^{2}}} = {p^{9} \over p^{\frac{2}{7}}} = p^{9 - \frac{2}{7}} = p^{8\frac{5}{7}}\)

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

\({\sqrt[6]{a^{5}} \over \sqrt[5]{a^{3}}} = {a^{\frac{5}{6}} \over a^{\frac{3}{5}}} = a^{\frac{5}{6} - \frac{3}{5}} = a^{\frac{7}{30}}\)

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

\(\sqrt[4]{p^{16}} = p^{\frac{16}{4}} = p^{4}\)

\({x^{6} \over x^{3} ⋅ \sqrt[5]{x^{4}}} = {x^{6} \over x^{3} ⋅ x^{\frac{4}{5}}} = {x^{6} \over x^{3\frac{4}{5}}} = x^{6 - 3\frac{4}{5}} = x^{2\frac{1}{5}}\)

\({2 y^{6} \over 9 x^{3}}\)

\((4 a)^{-3} = 4^{-3} ⋅ a^{-3} = {1 \over 4^{3}} ⋅ {1 \over a^{3}} = {1 \over 64 a^{3}}\)

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

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

\(\frac{3}{8} a^{-\frac{6}{7}} b^{\frac{1}{6}} = \frac{3}{8} ⋅ {1 \over a^{\frac{6}{7}}} ⋅ b^{\frac{1}{6}} = {3 ⋅ \sqrt[6]{b} \over 8 ⋅ \sqrt[7]{a^{6}}}\)