\({1 \over a^{2}} = a^{-2}\)

\({p^{2} \over p^{-4}} = p^{2 - -4} = p^{6}\)

\(x^{8} ⋅ x^{-9} = x^{8 + -9} = x^{-1}\)

\((x^{7})^{-5} = x^{7 ⋅ -5} = x^{-35}\)

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

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

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

\({6 \over a^{2}}\)

\({4 x^{3} \over 9 x^{4}} = {4 \over 9} ⋅ {x^{3} \over x^{4}} = {4 \over 9} ⋅ x^{3 - 4} = {4 \over 9} x^{-1}\)

\({a^{7} \over ({1 \over a^{9}})} = {a^{7} \over a^{-9}} = a^{7 - -9} = a^{16}\)

\({9 x^{3} y \over 4 x^{2} y^{2}} = {9 \over 4} ⋅ {x^{3} \over x^{2}} ⋅ {y^{1} \over y^{2}} = {9 \over 4} ⋅ x^{3 - 2} ⋅ x^{1 - 2} = 2\frac{1}{4} x y^{-1}\)

\(x^{8} ⋅ \sqrt[5]{x} = x^{8} ⋅ x^{\frac{1}{5}} = x^{8 + \frac{1}{5}} = x^{8\frac{1}{5}}\)

\(a^{4} ⋅ \sqrt[7]{a^{5}} = a^{4} ⋅ a^{\frac{5}{7}} = a^{4 + \frac{5}{7}} = a^{4\frac{5}{7}}\)

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

\({1 \over a^{7}} ⋅ \sqrt[9]{a^{7}} = a^{-7} ⋅ a^{\frac{7}{9}} = a^{-7 + \frac{7}{9}} = a^{-6\frac{2}{9}}\)

\({\sqrt[7]{a^{4}} \over \sqrt[7]{a^{3}}} = {a^{\frac{4}{7}} \over a^{\frac{3}{7}}} = a^{\frac{4}{7} - \frac{3}{7}} = a^{\frac{1}{7}}\)

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

\(\sqrt{p^{10}} = p^{\frac{10}{2}} = p^{5}\)

\({a^{4} \over a^{2} ⋅ \sqrt[9]{a^{8}}} = {a^{4} \over a^{2} ⋅ a^{\frac{8}{9}}} = {a^{4} \over a^{2\frac{8}{9}}} = a^{4 - 2\frac{8}{9}} = a^{1\frac{1}{9}}\)

\({4 q^{8} \over 5 p^{6}}\)

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

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

\(9 x^{5\frac{4}{7}} = 9 ⋅ x^{5} ⋅ x^{\frac{4}{7}} = 9 x^{5} ⋅ \sqrt[7]{x^{4}}\)

\(\frac{4}{7} a^{-\frac{3}{8}} b^{\frac{3}{7}} = \frac{4}{7} ⋅ {1 \over a^{\frac{3}{8}}} ⋅ b^{\frac{3}{7}} = {4 ⋅ \sqrt[7]{b^{3}} \over 7 ⋅ \sqrt[8]{a^{3}}}\)