Negatieve en gebroken exponenten

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

\({7 x^{2} \over 9 x^{4}} = {7 \over 9} ⋅ {x^{2} \over x^{4}} = {7 \over 9} ⋅ x^{2 - 4} = {7 \over 9} x^{-2}\)

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

\({({1 \over a^{6}}) \over a^{2}} = {a^{-6} \over a^{2}} = a^{-6 - 2} = a^{-8}\)

\({a^{4} \over ({1 \over a^{7}})} = {a^{4} \over a^{-7}} = a^{4 - -7} = a^{11}\)

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

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

\((a^{3})^{-5} = a^{3 ⋅ -5} = a^{-15}\)

\(p^{4} ⋅ p^{-5} = p^{4 + -5} = p^{-1}\)

\(x^{5} ⋅ {1 \over x^{6}} = x^{5} ⋅ x^{-6} = x^{5 + -6} = x^{-1}\)

\(x^{2} ⋅ \sqrt[8]{x} = x^{2} ⋅ x^{\frac{1}{8}} = x^{2 + \frac{1}{8}} = x^{2\frac{1}{8}}\)

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

\({a^{8} \over \sqrt[9]{a^{8}}} = {a^{8} \over a^{\frac{8}{9}}} = a^{8 - \frac{8}{9}} = a^{7\frac{1}{9}}\)

\({1 \over p^{2}} ⋅ \sqrt[9]{p^{4}} = p^{-2} ⋅ p^{\frac{4}{9}} = p^{-2 + \frac{4}{9}} = p^{-1\frac{5}{9}}\)

\({\sqrt[7]{x^{6}} \over \sqrt[7]{x^{3}}} = {x^{\frac{6}{7}} \over x^{\frac{3}{7}}} = x^{\frac{6}{7} - \frac{3}{7}} = x^{\frac{3}{7}}\)

\(\sqrt[7]{{1 \over x^{6}}} = \sqrt[7]{x^{-6}} = x^{-\frac{6}{7}}\)

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

\({p^{7} \over p^{4} ⋅ \sqrt[9]{p^{8}}} = {p^{7} \over p^{4} ⋅ p^{\frac{8}{9}}} = {p^{7} \over p^{4\frac{8}{9}}} = p^{7 - 4\frac{8}{9}} = p^{2\frac{1}{9}}\)

\((2 a)^{-3} = 2^{-3} ⋅ a^{-3} = {1 \over 2^{3}} ⋅ {1 \over a^{3}} = {1 \over 8 a^{3}}\)

\(({1 \over 4} x)^{-5} = (4^{-1} ⋅ x)^{-5} = (4^{-1})^{-5} ⋅ x^{-5} = 4^{5} ⋅ x^{-5} = {1\,024 \over x^{5}}\)

\({9 \over x^{6}}\)

\({3 b^{8} \over 8 a^{4}}\)

\(4 p^{7\frac{5}{7}} = 4 ⋅ p^{7} ⋅ p^{\frac{5}{7}} = 4 p^{7} ⋅ \sqrt[7]{p^{5}}\)

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