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

\({a^{8} \over a^{-7}} = a^{8 - -7} = a^{15}\)

\(a^{6} ⋅ a^{-9} = a^{6 + -9} = a^{-3}\)

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

\(p^{7} ⋅ {1 \over p^{8}} = p^{7} ⋅ p^{-8} = p^{7 + -8} = p^{-1}\)

\({({1 \over a^{8}}) \over a^{3}} = {a^{-8} \over a^{3}} = a^{-8 - 3} = a^{-11}\)

\({a^{2} \over a^{0}} = a^{2 - 0} = a^{2}\)

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

\({4 p^{4} \over 9 p^{7}} = {4 \over 9} ⋅ {p^{4} \over p^{7}} = {4 \over 9} ⋅ p^{4 - 7} = {4 \over 9} p^{-3}\)

\({x^{2} \over ({1 \over x^{5}})} = {x^{2} \over x^{-5}} = x^{2 - -5} = x^{7}\)

\({7 x^{8} y \over 6 x^{3} y^{5}} = {7 \over 6} ⋅ {x^{8} \over x^{3}} ⋅ {y^{1} \over y^{5}} = {7 \over 6} ⋅ x^{8 - 3} ⋅ x^{1 - 5} = 1\frac{1}{6} x^{5} y^{-4}\)

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

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

\({p^{3} \over \sqrt[9]{p^{5}}} = {p^{3} \over p^{\frac{5}{9}}} = p^{3 - \frac{5}{9}} = p^{2\frac{4}{9}}\)

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

\({\sqrt[9]{x^{8}} \over \sqrt[3]{x^{2}}} = {x^{\frac{8}{9}} \over x^{\frac{2}{3}}} = x^{\frac{8}{9} - \frac{2}{3}} = x^{\frac{2}{9}}\)

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

\(\sqrt{p^{6}} = p^{\frac{6}{2}} = p^{3}\)

\({x^{4} \over x^{2} ⋅ \sqrt[8]{x^{3}}} = {x^{4} \over x^{2} ⋅ x^{\frac{3}{8}}} = {x^{4} \over x^{2\frac{3}{8}}} = x^{4 - 2\frac{3}{8}} = x^{1\frac{5}{8}}\)

\({2 y^{7} \over 5 x^{4}}\)

\((5 a)^{-4} = 5^{-4} ⋅ a^{-4} = {1 \over 5^{4}} ⋅ {1 \over a^{4}} = {1 \over 625 a^{4}}\)

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

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

\(\frac{8}{9} a^{-\frac{2}{7}} b^{\frac{3}{4}} = \frac{8}{9} ⋅ {1 \over a^{\frac{2}{7}}} ⋅ b^{\frac{3}{4}} = {8 ⋅ \sqrt[4]{b^{3}} \over 9 ⋅ \sqrt[7]{a^{2}}}\)