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

\({x^{5} \over x^{-9}} = x^{5 - -9} = x^{14}\)

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

\((x^{4})^{-8} = x^{4 ⋅ -8} = x^{-32}\)

\(p^{6} ⋅ {1 \over p^{8}} = p^{6} ⋅ p^{-8} = p^{6 + -8} = p^{-2}\)

\({({1 \over x^{8}}) \over x^{7}} = {x^{-8} \over x^{7}} = x^{-8 - 7} = x^{-15}\)

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

\({5 \over a^{8}}\)

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

\({a^{6} \over ({1 \over a^{8}})} = {a^{6} \over a^{-8}} = a^{6 - -8} = a^{14}\)

\({8 x^{5} y^{3} \over 7 x^{3} y^{4}} = {8 \over 7} ⋅ {x^{5} \over x^{3}} ⋅ {y^{3} \over y^{4}} = {8 \over 7} ⋅ x^{5 - 3} ⋅ x^{3 - 4} = 1\frac{1}{7} x^{2} y^{-1}\)

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

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

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

\({1 \over a^{7}} ⋅ \sqrt[9]{a^{5}} = a^{-7} ⋅ a^{\frac{5}{9}} = a^{-7 + \frac{5}{9}} = a^{-6\frac{4}{9}}\)

\({\sqrt[9]{x^{4}} \over \sqrt[8]{x^{3}}} = {x^{\frac{4}{9}} \over x^{\frac{3}{8}}} = x^{\frac{4}{9} - \frac{3}{8}} = x^{\frac{5}{72}}\)

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

\(\sqrt[4]{a^{8}} = a^{\frac{8}{4}} = a^{2}\)

\({x^{5} \over x^{8} ⋅ \sqrt[9]{x^{7}}} = {x^{5} \over x^{8} ⋅ x^{\frac{7}{9}}} = {x^{5} \over x^{8\frac{7}{9}}} = x^{5 - 8\frac{7}{9}} = x^{-3\frac{7}{9}}\)

\({3 b^{3} \over 7 a^{2}}\)

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

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

\(2 a^{4\frac{3}{8}} = 2 ⋅ a^{4} ⋅ a^{\frac{3}{8}} = 2 a^{4} ⋅ \sqrt[8]{a^{3}}\)

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