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

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

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

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

\(x^{6} ⋅ {1 \over x^{9}} = x^{6} ⋅ x^{-9} = x^{6 + -9} = x^{-3}\)

\({({1 \over a^{4}}) \over a^{2}} = {a^{-4} \over a^{2}} = a^{-4 - 2} = a^{-6}\)

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

\({9 \over x^{7}}\)

\({3 x^{3} \over 8 x^{6}} = {3 \over 8} ⋅ {x^{3} \over x^{6}} = {3 \over 8} ⋅ x^{3 - 6} = {3 \over 8} x^{-3}\)

\({a^{5} \over ({1 \over a^{8}})} = {a^{5} \over a^{-8}} = a^{5 - -8} = a^{13}\)

\({9 x^{8} y^{2} \over 4 x^{4} y^{4}} = {9 \over 4} ⋅ {x^{8} \over x^{4}} ⋅ {y^{2} \over y^{4}} = {9 \over 4} ⋅ x^{8 - 4} ⋅ x^{2 - 4} = 2\frac{1}{4} x^{4} y^{-2}\)

\(a^{2} ⋅ \sqrt[9]{a} = a^{2} ⋅ a^{\frac{1}{9}} = a^{2 + \frac{1}{9}} = a^{2\frac{1}{9}}\)

\(p^{4} ⋅ \sqrt[8]{p^{3}} = p^{4} ⋅ p^{\frac{3}{8}} = p^{4 + \frac{3}{8}} = p^{4\frac{3}{8}}\)

\({x^{4} \over \sqrt[8]{x^{7}}} = {x^{4} \over x^{\frac{7}{8}}} = x^{4 - \frac{7}{8}} = x^{3\frac{1}{8}}\)

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

\({\sqrt[8]{a^{7}} \over \sqrt[7]{a^{2}}} = {a^{\frac{7}{8}} \over a^{\frac{2}{7}}} = a^{\frac{7}{8} - \frac{2}{7}} = a^{\frac{33}{56}}\)

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

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

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

\({5 b^{4} \over 9 a^{6}}\)

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

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

\(7 x^{3\frac{8}{9}} = 7 ⋅ x^{3} ⋅ x^{\frac{8}{9}} = 7 x^{3} ⋅ \sqrt[9]{x^{8}}\)

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