Negatieve en gebroken exponenten

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

\({5 a^{5} \over 7 a^{9}} = {5 \over 7} ⋅ {a^{5} \over a^{9}} = {5 \over 7} ⋅ a^{5 - 9} = {5 \over 7} a^{-4}\)

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

\({({1 \over x^{9}}) \over x^{8}} = {x^{-9} \over x^{8}} = x^{-9 - 8} = x^{-17}\)

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

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

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

\((a^{5})^{-4} = a^{5 ⋅ -4} = a^{-20}\)

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

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

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

\(x^{8} ⋅ \sqrt[9]{x^{5}} = x^{8} ⋅ x^{\frac{5}{9}} = x^{8 + \frac{5}{9}} = x^{8\frac{5}{9}}\)

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

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

\({\sqrt[8]{x^{7}} \over \sqrt[8]{x^{5}}} = {x^{\frac{7}{8}} \over x^{\frac{5}{8}}} = x^{\frac{7}{8} - \frac{5}{8}} = x^{\frac{1}{4}}\)

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

\(\sqrt{x^{8}} = x^{\frac{8}{2}} = x^{4}\)

\({p^{8} \over p^{4} ⋅ \sqrt[9]{p^{8}}} = {p^{8} \over p^{4} ⋅ p^{\frac{8}{9}}} = {p^{8} \over p^{4\frac{8}{9}}} = p^{8 - 4\frac{8}{9}} = p^{3\frac{1}{9}}\)

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

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

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

\({3 b^{5} \over 5 a^{6}}\)

\(2 a^{3\frac{3}{7}} = 2 ⋅ a^{3} ⋅ a^{\frac{3}{7}} = 2 a^{3} ⋅ \sqrt[7]{a^{3}}\)

\(\frac{3}{8} p^{-\frac{5}{7}} q^{\frac{4}{5}} = \frac{3}{8} ⋅ {1 \over p^{\frac{5}{7}}} ⋅ q^{\frac{4}{5}} = {3 ⋅ \sqrt[5]{q^{4}} \over 8 ⋅ \sqrt[7]{p^{5}}}\)