Negatieve en gebroken exponenten

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

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

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

\({({1 \over x^{9}}) \over x^{6}} = {x^{-9} \over x^{6}} = x^{-9 - 6} = x^{-15}\)

\({p^{3} \over ({1 \over p^{9}})} = {p^{3} \over p^{-9}} = p^{3 - -9} = p^{12}\)

\({9 a^{4} b^{5} \over 2 a b^{6}} = {9 \over 2} ⋅ {a^{4} \over a^{1}} ⋅ {b^{5} \over b^{6}} = {9 \over 2} ⋅ a^{4 - 1} ⋅ a^{5 - 6} = 4\frac{1}{2} a^{3} b^{-1}\)

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

\((x^{5})^{-7} = x^{5 ⋅ -7} = x^{-35}\)

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

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

\(x^{2} ⋅ \sqrt[7]{x} = x^{2} ⋅ x^{\frac{1}{7}} = x^{2 + \frac{1}{7}} = x^{2\frac{1}{7}}\)

\(x^{4} ⋅ \sqrt[3]{x^{2}} = x^{4} ⋅ x^{\frac{2}{3}} = x^{4 + \frac{2}{3}} = x^{4\frac{2}{3}}\)

\({p^{7} \over \sqrt[9]{p^{7}}} = {p^{7} \over p^{\frac{7}{9}}} = p^{7 - \frac{7}{9}} = p^{6\frac{2}{9}}\)

\({1 \over a^{2}} ⋅ \sqrt[5]{a^{3}} = a^{-2} ⋅ a^{\frac{3}{5}} = a^{-2 + \frac{3}{5}} = a^{-1\frac{2}{5}}\)

\({\sqrt[6]{a^{5}} \over \sqrt[7]{a^{4}}} = {a^{\frac{5}{6}} \over a^{\frac{4}{7}}} = a^{\frac{5}{6} - \frac{4}{7}} = a^{\frac{11}{42}}\)

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

\(\sqrt{a^{10}} = a^{\frac{10}{2}} = a^{5}\)

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

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

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

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

\({6 y^{4} \over 7 x^{2}}\)

\(5 x^{9\frac{4}{7}} = 5 ⋅ x^{9} ⋅ x^{\frac{4}{7}} = 5 x^{9} ⋅ \sqrt[7]{x^{4}}\)

\(\frac{1}{4} a^{-\frac{7}{8}} b^{\frac{6}{7}} = \frac{1}{4} ⋅ {1 \over a^{\frac{7}{8}}} ⋅ b^{\frac{6}{7}} = {1 ⋅ \sqrt[7]{b^{6}} \over 4 ⋅ \sqrt[8]{a^{7}}}\)