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

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

\(a^{3} ⋅ a^{-8} = a^{3 + -8} = a^{-5}\)

\((a^{9})^{-2} = a^{9 ⋅ -2} = a^{-18}\)

\(x^{3} ⋅ {1 \over x^{7}} = x^{3} ⋅ x^{-7} = x^{3 + -7} = x^{-4}\)

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

\({a^{0} \over a^{9}} = a^{0 - 9} = a^{-9}\)

\({6 \over x^{2}}\)

\({3 a^{2} \over 7 a^{4}} = {3 \over 7} ⋅ {a^{2} \over a^{4}} = {3 \over 7} ⋅ a^{2 - 4} = {3 \over 7} a^{-2}\)

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

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

\(p^{7} ⋅ \sqrt[4]{p} = p^{7} ⋅ p^{\frac{1}{4}} = p^{7 + \frac{1}{4}} = p^{7\frac{1}{4}}\)

\(x^{6} ⋅ \sqrt[9]{x^{4}} = x^{6} ⋅ x^{\frac{4}{9}} = x^{6 + \frac{4}{9}} = x^{6\frac{4}{9}}\)

\({a^{9} \over \sqrt[6]{a^{5}}} = {a^{9} \over a^{\frac{5}{6}}} = a^{9 - \frac{5}{6}} = a^{8\frac{1}{6}}\)

\({1 \over a^{4}} ⋅ \sqrt[7]{a^{2}} = a^{-4} ⋅ a^{\frac{2}{7}} = a^{-4 + \frac{2}{7}} = a^{-3\frac{5}{7}}\)

\({\sqrt[3]{a^{2}} \over \sqrt[7]{a^{2}}} = {a^{\frac{2}{3}} \over a^{\frac{2}{7}}} = a^{\frac{2}{3} - \frac{2}{7}} = a^{\frac{8}{21}}\)

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

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

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

\({5 y^{6} \over 8 x^{4}}\)

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

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

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

\(\frac{7}{9} a^{-\frac{7}{8}} b^{\frac{4}{5}} = \frac{7}{9} ⋅ {1 \over a^{\frac{7}{8}}} ⋅ b^{\frac{4}{5}} = {7 ⋅ \sqrt[5]{b^{4}} \over 9 ⋅ \sqrt[8]{a^{7}}}\)