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

\({7 a \over 9 a^{5}} = {7 \over 9} ⋅ {a \over a^{5}} = {7 \over 9} ⋅ a^{1 - 5} = {7 \over 9} a^{-4}\)

\({p^{6} \over p^{-3}} = p^{6 - -3} = p^{9}\)

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

\((x^{5})^{-2} = x^{5 ⋅ -2} = x^{-10}\)

\(x^{4} ⋅ {1 \over x^{6}} = x^{4} ⋅ x^{-6} = x^{4 + -6} = x^{-2}\)

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

\({3 \over p^{6}}\)

\((5 a)^{-3} = 5^{-3} ⋅ a^{-3} = {1 \over 5^{3}} ⋅ {1 \over a^{3}} = {1 \over 125 a^{3}}\)

\(a^{9} ⋅ \sqrt[9]{a} = a^{9} ⋅ a^{\frac{1}{9}} = a^{9 + \frac{1}{9}} = a^{9\frac{1}{9}}\)

\(p^{6} ⋅ \sqrt[9]{p^{2}} = p^{6} ⋅ p^{\frac{2}{9}} = p^{6 + \frac{2}{9}} = p^{6\frac{2}{9}}\)

\({x^{8} \over \sqrt[7]{x^{6}}} = {x^{8} \over x^{\frac{6}{7}}} = x^{8 - \frac{6}{7}} = x^{7\frac{1}{7}}\)

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

\({\sqrt[7]{a^{4}} \over \sqrt[9]{a^{5}}} = {a^{\frac{4}{7}} \over a^{\frac{5}{9}}} = a^{\frac{4}{7} - \frac{5}{9}} = a^{\frac{1}{63}}\)

\(\sqrt{x^{8}} = x^{\frac{8}{2}} = x^{4}\)

\({a^{8} \over a^{9} ⋅ \sqrt[8]{a^{5}}} = {a^{8} \over a^{9} ⋅ a^{\frac{5}{8}}} = {a^{8} \over a^{9\frac{5}{8}}} = a^{8 - 9\frac{5}{8}} = a^{-1\frac{5}{8}}\)

\(3 p^{4\frac{3}{4}} = 3 ⋅ p^{4} ⋅ p^{\frac{3}{4}} = 3 p^{4} ⋅ \sqrt[4]{p^{3}}\)