Negatieve en gebroken exponenten

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

\({3 x^{5} \over 5 x^{10}} = {3 \over 5} ⋅ {x^{5} \over x^{10}} = {3 \over 5} ⋅ x^{5 - 10} = {3 \over 5} x^{-5}\)

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

\({({1 \over a^{9}}) \over a^{5}} = {a^{-9} \over a^{5}} = a^{-9 - 5} = a^{-14}\)

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

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

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

\((a^{2})^{-7} = a^{2 ⋅ -7} = a^{-14}\)

\(a^{3} ⋅ a^{-6} = a^{3 + -6} = a^{-3}\)

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

\(a^{9} ⋅ \sqrt[7]{a} = a^{9} ⋅ a^{\frac{1}{7}} = a^{9 + \frac{1}{7}} = a^{9\frac{1}{7}}\)

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

\({a^{6} \over \sqrt[6]{a^{5}}} = {a^{6} \over a^{\frac{5}{6}}} = a^{6 - \frac{5}{6}} = a^{5\frac{1}{6}}\)

\({1 \over a^{4}} ⋅ \sqrt[6]{a^{5}} = a^{-4} ⋅ a^{\frac{5}{6}} = a^{-4 + \frac{5}{6}} = a^{-3\frac{1}{6}}\)

\({\sqrt[8]{a^{5}} \over \sqrt[5]{a^{3}}} = {a^{\frac{5}{8}} \over a^{\frac{3}{5}}} = a^{\frac{5}{8} - \frac{3}{5}} = a^{\frac{1}{40}}\)

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

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

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

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

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

\({7 \over a^{2}}\)

\({3 b^{7} \over 7 a^{6}}\)

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

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