Negatieve en gebroken exponenten

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

\({3 x^{3} \over 8 x^{7}} = {3 \over 8} ⋅ {x^{3} \over x^{7}} = {3 \over 8} ⋅ x^{3 - 7} = {3 \over 8} x^{-4}\)

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

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

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

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

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

\((a^{3})^{-7} = a^{3 ⋅ -7} = a^{-21}\)

\(x^{5} ⋅ x^{-9} = x^{5 + -9} = x^{-4}\)

\(a^{3} ⋅ {1 \over a^{8}} = a^{3} ⋅ a^{-8} = a^{3 + -8} = a^{-5}\)

\(a^{9} ⋅ \sqrt[6]{a} = a^{9} ⋅ a^{\frac{1}{6}} = a^{9 + \frac{1}{6}} = a^{9\frac{1}{6}}\)

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

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

\({1 \over a^{2}} ⋅ \sqrt[9]{a^{8}} = a^{-2} ⋅ a^{\frac{8}{9}} = a^{-2 + \frac{8}{9}} = a^{-1\frac{1}{9}}\)

\({\sqrt[9]{x^{7}} \over \sqrt[8]{x^{5}}} = {x^{\frac{7}{9}} \over x^{\frac{5}{8}}} = x^{\frac{7}{9} - \frac{5}{8}} = x^{\frac{11}{72}}\)

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

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

\({x^{2} \over x^{8} ⋅ \sqrt[7]{x^{4}}} = {x^{2} \over x^{8} ⋅ x^{\frac{4}{7}}} = {x^{2} \over x^{8\frac{4}{7}}} = x^{2 - 8\frac{4}{7}} = x^{-6\frac{4}{7}}\)

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

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

\({9 \over p^{8}}\)

\({6 y^{9} \over 7 x^{4}}\)

\(9 p^{3\frac{4}{9}} = 9 ⋅ p^{3} ⋅ p^{\frac{4}{9}} = 9 p^{3} ⋅ \sqrt[9]{p^{4}}\)

\(\frac{1}{9} x^{-\frac{4}{5}} y^{\frac{1}{8}} = \frac{1}{9} ⋅ {1 \over x^{\frac{4}{5}}} ⋅ y^{\frac{1}{8}} = {1 ⋅ \sqrt[8]{y} \over 9 ⋅ \sqrt[5]{x^{4}}}\)