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

\({5 p \over 7 p^{3}} = {5 \over 7} ⋅ {p \over p^{3}} = {5 \over 7} ⋅ p^{1 - 3} = {5 \over 7} p^{-2}\)

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

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

\((a^{5})^{-6} = a^{5 ⋅ -6} = a^{-30}\)

\(x^{5} ⋅ {1 \over x^{6}} = x^{5} ⋅ x^{-6} = x^{5 + -6} = x^{-1}\)

\({({1 \over a^{7}}) \over a^{6}} = {a^{-7} \over a^{6}} = a^{-7 - 6} = a^{-13}\)

\({a^{4} \over ({1 \over a^{7}})} = {a^{4} \over a^{-7}} = a^{4 - -7} = a^{11}\)

\({7 x^{3} y^{2} \over 3 x y^{6}} = {7 \over 3} ⋅ {x^{3} \over x^{1}} ⋅ {y^{2} \over y^{6}} = {7 \over 3} ⋅ x^{3 - 1} ⋅ x^{2 - 6} = 2\frac{1}{3} x^{2} y^{-4}\)

\({p^{3} \over p^{0}} = p^{3 - 0} = p^{3}\)

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

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

\({a^{7} \over \sqrt[6]{a^{5}}} = {a^{7} \over a^{\frac{5}{6}}} = a^{7 - \frac{5}{6}} = a^{6\frac{1}{6}}\)

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

\({\sqrt[9]{a^{8}} \over \sqrt[8]{a^{3}}} = {a^{\frac{8}{9}} \over a^{\frac{3}{8}}} = a^{\frac{8}{9} - \frac{3}{8}} = a^{\frac{37}{72}}\)

\(\sqrt[9]{{1 \over x^{2}}} = \sqrt[9]{x^{-2}} = x^{-\frac{2}{9}}\)

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

\({a^{7} \over a^{4} ⋅ \sqrt[3]{a^{2}}} = {a^{7} \over a^{4} ⋅ a^{\frac{2}{3}}} = {a^{7} \over a^{4\frac{2}{3}}} = a^{7 - 4\frac{2}{3}} = a^{2\frac{1}{3}}\)

\({5 \over p^{4}}\)

\({2 y^{8} \over 9 x^{9}}\)

\((2 x)^{-4} = 2^{-4} ⋅ x^{-4} = {1 \over 2^{4}} ⋅ {1 \over x^{4}} = {1 \over 16 x^{4}}\)

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

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

\(\frac{1}{5} a^{-\frac{6}{7}} b^{\frac{5}{7}} = \frac{1}{5} ⋅ {1 \over a^{\frac{6}{7}}} ⋅ b^{\frac{5}{7}} = {1 ⋅ \sqrt[7]{b^{5}} \over 5 ⋅ \sqrt[7]{a^{6}}}\)