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

\({p^{9} \over p^{-8}} = p^{9 - -8} = p^{17}\)

\(a^{3} ⋅ a^{-7} = a^{3 + -7} = a^{-4}\)

\((x^{7})^{-6} = x^{7 ⋅ -6} = x^{-42}\)

\(x^{2} ⋅ {1 \over x^{9}} = x^{2} ⋅ x^{-9} = x^{2 + -9} = x^{-7}\)

\({({1 \over a^{8}}) \over a^{4}} = {a^{-8} \over a^{4}} = a^{-8 - 4} = a^{-12}\)

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

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

\({6 a^{5} \over 7 a^{7}} = {6 \over 7} ⋅ {a^{5} \over a^{7}} = {6 \over 7} ⋅ a^{5 - 7} = {6 \over 7} a^{-2}\)

\({x^{2} \over ({1 \over x^{7}})} = {x^{2} \over x^{-7}} = x^{2 - -7} = x^{9}\)

\({7 a^{6} b^{2} \over 2 a^{3} b^{7}} = {7 \over 2} ⋅ {a^{6} \over a^{3}} ⋅ {b^{2} \over b^{7}} = {7 \over 2} ⋅ a^{6 - 3} ⋅ a^{2 - 7} = 3\frac{1}{2} a^{3} b^{-5}\)

\(x^{2} ⋅ \sqrt[4]{x} = x^{2} ⋅ x^{\frac{1}{4}} = x^{2 + \frac{1}{4}} = x^{2\frac{1}{4}}\)

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

\({x^{3} \over \sqrt[9]{x^{7}}} = {x^{3} \over x^{\frac{7}{9}}} = x^{3 - \frac{7}{9}} = x^{2\frac{2}{9}}\)

\({1 \over p^{9}} ⋅ \sqrt[7]{p^{6}} = p^{-9} ⋅ p^{\frac{6}{7}} = p^{-9 + \frac{6}{7}} = p^{-8\frac{1}{7}}\)

\({\sqrt[8]{p^{7}} \over \sqrt[5]{p^{4}}} = {p^{\frac{7}{8}} \over p^{\frac{4}{5}}} = p^{\frac{7}{8} - \frac{4}{5}} = p^{\frac{3}{40}}\)

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

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

\({x^{9} \over x^{2} ⋅ \sqrt[8]{x^{5}}} = {x^{9} \over x^{2} ⋅ x^{\frac{5}{8}}} = {x^{9} \over x^{2\frac{5}{8}}} = x^{9 - 2\frac{5}{8}} = x^{6\frac{3}{8}}\)

\({5 y^{2} \over 8 x^{9}}\)

\((4 p)^{-3} = 4^{-3} ⋅ p^{-3} = {1 \over 4^{3}} ⋅ {1 \over p^{3}} = {1 \over 64 p^{3}}\)

\(({1 \over 5} a)^{-3} = (5^{-1} ⋅ a)^{-3} = (5^{-1})^{-3} ⋅ a^{-3} = 5^{3} ⋅ a^{-3} = {125 \over a^{3}}\)

\(6 a^{4\frac{6}{7}} = 6 ⋅ a^{4} ⋅ a^{\frac{6}{7}} = 6 a^{4} ⋅ \sqrt[7]{a^{6}}\)

\(\frac{4}{5} a^{-\frac{3}{7}} b^{\frac{1}{5}} = \frac{4}{5} ⋅ {1 \over a^{\frac{3}{7}}} ⋅ b^{\frac{1}{5}} = {4 ⋅ \sqrt[5]{b} \over 5 ⋅ \sqrt[7]{a^{3}}}\)