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

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

\(x^{2} ⋅ x^{-8} = x^{2 + -8} = x^{-6}\)

\((x^{7})^{-8} = x^{7 ⋅ -8} = x^{-56}\)

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

\({({1 \over a^{9}}) \over a^{6}} = {a^{-9} \over a^{6}} = a^{-9 - 6} = a^{-15}\)

\({p^{7} \over p^{0}} = p^{7 - 0} = p^{7}\)

\({7 \over a^{3}}\)

\({3 x^{4} \over 4 x^{5}} = {3 \over 4} ⋅ {x^{4} \over x^{5}} = {3 \over 4} ⋅ x^{4 - 5} = {3 \over 4} x^{-1}\)

\({a^{3} \over ({1 \over a^{4}})} = {a^{3} \over a^{-4}} = a^{3 - -4} = a^{7}\)

\({5 x^{4} y^{3} \over 4 x y^{7}} = {5 \over 4} ⋅ {x^{4} \over x^{1}} ⋅ {y^{3} \over y^{7}} = {5 \over 4} ⋅ x^{4 - 1} ⋅ x^{3 - 7} = 1\frac{1}{4} x^{3} y^{-4}\)

\(a^{2} ⋅ \sqrt[3]{a} = a^{2} ⋅ a^{\frac{1}{3}} = a^{2 + \frac{1}{3}} = a^{2\frac{1}{3}}\)

\(p^{3} ⋅ \sqrt[9]{p^{4}} = p^{3} ⋅ p^{\frac{4}{9}} = p^{3 + \frac{4}{9}} = p^{3\frac{4}{9}}\)

\({x^{5} \over \sqrt[9]{x^{8}}} = {x^{5} \over x^{\frac{8}{9}}} = x^{5 - \frac{8}{9}} = x^{4\frac{1}{9}}\)

\({1 \over a^{4}} ⋅ \sqrt[9]{a^{4}} = a^{-4} ⋅ a^{\frac{4}{9}} = a^{-4 + \frac{4}{9}} = a^{-3\frac{5}{9}}\)

\({\sqrt[3]{p^{2}} \over \sqrt[8]{p^{3}}} = {p^{\frac{2}{3}} \over p^{\frac{3}{8}}} = p^{\frac{2}{3} - \frac{3}{8}} = p^{\frac{7}{24}}\)

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

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

\({a^{3} \over a^{9} ⋅ \sqrt[7]{a^{6}}} = {a^{3} \over a^{9} ⋅ a^{\frac{6}{7}}} = {a^{3} \over a^{9\frac{6}{7}}} = a^{3 - 9\frac{6}{7}} = a^{-6\frac{6}{7}}\)

\({5 y^{3} \over 7 x^{9}}\)

\((3 a)^{-5} = 3^{-5} ⋅ a^{-5} = {1 \over 3^{5}} ⋅ {1 \over a^{5}} = {1 \over 243 a^{5}}\)

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

\(7 x^{4\frac{2}{9}} = 7 ⋅ x^{4} ⋅ x^{\frac{2}{9}} = 7 x^{4} ⋅ \sqrt[9]{x^{2}}\)

\(\frac{1}{7} a^{-\frac{1}{6}} b^{\frac{5}{8}} = \frac{1}{7} ⋅ {1 \over a^{\frac{1}{6}}} ⋅ b^{\frac{5}{8}} = {1 ⋅ \sqrt[8]{b^{5}} \over 7 ⋅ \sqrt[6]{a}}\)