Negatieve en gebroken exponenten

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

\({2 x^{5} \over 3 x^{9}} = {2 \over 3} ⋅ {x^{5} \over x^{9}} = {2 \over 3} ⋅ x^{5 - 9} = {2 \over 3} x^{-4}\)

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

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

\({a^{2} \over ({1 \over a^{8}})} = {a^{2} \over a^{-8}} = a^{2 - -8} = a^{10}\)

\({8 x^{3} y^{5} \over 5 x y^{9}} = {8 \over 5} ⋅ {x^{3} \over x^{1}} ⋅ {y^{5} \over y^{9}} = {8 \over 5} ⋅ x^{3 - 1} ⋅ x^{5 - 9} = 1\frac{3}{5} x^{2} y^{-4}\)

\({x^{0} \over x^{6}} = x^{0 - 6} = x^{-6}\)

\((a^{5})^{-8} = a^{5 ⋅ -8} = a^{-40}\)

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

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

\(a^{9} ⋅ \sqrt[3]{a} = a^{9} ⋅ a^{\frac{1}{3}} = a^{9 + \frac{1}{3}} = a^{9\frac{1}{3}}\)

\(a^{2} ⋅ \sqrt[8]{a^{7}} = a^{2} ⋅ a^{\frac{7}{8}} = a^{2 + \frac{7}{8}} = a^{2\frac{7}{8}}\)

\({p^{5} \over \sqrt[9]{p^{7}}} = {p^{5} \over p^{\frac{7}{9}}} = p^{5 - \frac{7}{9}} = p^{4\frac{2}{9}}\)

\({1 \over x^{4}} ⋅ \sqrt[9]{x^{4}} = x^{-4} ⋅ x^{\frac{4}{9}} = x^{-4 + \frac{4}{9}} = x^{-3\frac{5}{9}}\)

\({\sqrt[9]{x^{5}} \over \sqrt[5]{x^{2}}} = {x^{\frac{5}{9}} \over x^{\frac{2}{5}}} = x^{\frac{5}{9} - \frac{2}{5}} = x^{\frac{7}{45}}\)

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

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

\({p^{8} \over p^{2} ⋅ \sqrt[7]{p^{6}}} = {p^{8} \over p^{2} ⋅ p^{\frac{6}{7}}} = {p^{8} \over p^{2\frac{6}{7}}} = p^{8 - 2\frac{6}{7}} = p^{5\frac{1}{7}}\)

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

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

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

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

\(6 a^{4\frac{7}{8}} = 6 ⋅ a^{4} ⋅ a^{\frac{7}{8}} = 6 a^{4} ⋅ \sqrt[8]{a^{7}}\)

\(\frac{7}{8} x^{-\frac{6}{7}} y^{\frac{2}{5}} = \frac{7}{8} ⋅ {1 \over x^{\frac{6}{7}}} ⋅ y^{\frac{2}{5}} = {7 ⋅ \sqrt[5]{y^{2}} \over 8 ⋅ \sqrt[7]{x^{6}}}\)