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

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

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

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

\(x^{3} ⋅ {1 \over x^{9}} = x^{3} ⋅ x^{-9} = x^{3 + -9} = x^{-6}\)

\({({1 \over a^{9}}) \over a^{3}} = {a^{-9} \over a^{3}} = a^{-9 - 3} = a^{-12}\)

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

\({4 \over p^{2}}\)

\({4 x^{2} \over 7 x^{6}} = {4 \over 7} ⋅ {x^{2} \over x^{6}} = {4 \over 7} ⋅ x^{2 - 6} = {4 \over 7} x^{-4}\)

\({a^{3} \over ({1 \over a^{6}})} = {a^{3} \over a^{-6}} = a^{3 - -6} = a^{9}\)

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

\(x^{4} ⋅ \sqrt[9]{x} = x^{4} ⋅ x^{\frac{1}{9}} = x^{4 + \frac{1}{9}} = x^{4\frac{1}{9}}\)

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

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

\({1 \over a^{9}} ⋅ \sqrt[5]{a^{2}} = a^{-9} ⋅ a^{\frac{2}{5}} = a^{-9 + \frac{2}{5}} = a^{-8\frac{3}{5}}\)

\({\sqrt[7]{a^{5}} \over \sqrt[9]{a^{2}}} = {a^{\frac{5}{7}} \over a^{\frac{2}{9}}} = a^{\frac{5}{7} - \frac{2}{9}} = a^{\frac{31}{63}}\)

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

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

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

\({2 y^{7} \over 9 x^{5}}\)

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

\(({1 \over 5} a)^{-2} = (5^{-1} ⋅ a)^{-2} = (5^{-1})^{-2} ⋅ a^{-2} = 5^{2} ⋅ a^{-2} = {25 \over a^{2}}\)

\(2 a^{3\frac{5}{9}} = 2 ⋅ a^{3} ⋅ a^{\frac{5}{9}} = 2 a^{3} ⋅ \sqrt[9]{a^{5}}\)

\(\frac{1}{5} a^{-\frac{2}{9}} b^{\frac{3}{5}} = \frac{1}{5} ⋅ {1 \over a^{\frac{2}{9}}} ⋅ b^{\frac{3}{5}} = {1 ⋅ \sqrt[5]{b^{3}} \over 5 ⋅ \sqrt[9]{a^{2}}}\)