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

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

\({x^{7} \over x^{-4}} = x^{7 - -4} = x^{11}\)

\(p^{3} ⋅ p^{-6} = p^{3 + -6} = p^{-3}\)

\((a^{7})^{-4} = a^{7 ⋅ -4} = a^{-28}\)

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

\({a^{0} \over a^{4}} = a^{0 - 4} = a^{-4}\)

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

\((3 p)^{-4} = 3^{-4} ⋅ p^{-4} = {1 \over 3^{4}} ⋅ {1 \over p^{4}} = {1 \over 81 p^{4}}\)

\(a^{3} ⋅ \sqrt[4]{a} = a^{3} ⋅ a^{\frac{1}{4}} = a^{3 + \frac{1}{4}} = a^{3\frac{1}{4}}\)

\(p^{5} ⋅ \sqrt[9]{p^{7}} = p^{5} ⋅ p^{\frac{7}{9}} = p^{5 + \frac{7}{9}} = p^{5\frac{7}{9}}\)

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

\({1 \over a^{9}} ⋅ \sqrt[7]{a^{2}} = a^{-9} ⋅ a^{\frac{2}{7}} = a^{-9 + \frac{2}{7}} = a^{-8\frac{5}{7}}\)

\({\sqrt[5]{x^{2}} \over \sqrt[7]{x^{2}}} = {x^{\frac{2}{5}} \over x^{\frac{2}{7}}} = x^{\frac{2}{5} - \frac{2}{7}} = x^{\frac{4}{35}}\)

\(\sqrt[3]{a^{12}} = a^{\frac{12}{3}} = a^{4}\)

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

\(2 a^{4\frac{3}{5}} = 2 ⋅ a^{4} ⋅ a^{\frac{3}{5}} = 2 a^{4} ⋅ \sqrt[5]{a^{3}}\)