Negatieve en gebroken exponenten

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

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

\({p^{3} \over p^{-5}} = p^{3 - -5} = p^{8}\)

\({({1 \over x^{7}}) \over x^{2}} = {x^{-7} \over x^{2}} = x^{-7 - 2} = x^{-9}\)

\({x^{6} \over ({1 \over x^{7}})} = {x^{6} \over x^{-7}} = x^{6 - -7} = x^{13}\)

\({8 p^{2} q^{2} \over 7 p q^{5}} = {8 \over 7} ⋅ {p^{2} \over p^{1}} ⋅ {q^{2} \over q^{5}} = {8 \over 7} ⋅ p^{2 - 1} ⋅ p^{2 - 5} = 1\frac{1}{7} p q^{-3}\)

\({a^{3} \over a^{0}} = a^{3 - 0} = a^{3}\)

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

\(x^{2} ⋅ x^{-3} = x^{2 + -3} = x^{-1}\)

\(a^{8} ⋅ {1 \over a^{9}} = a^{8} ⋅ a^{-9} = a^{8 + -9} = a^{-1}\)

\(x^{3} ⋅ \sqrt[5]{x} = x^{3} ⋅ x^{\frac{1}{5}} = x^{3 + \frac{1}{5}} = x^{3\frac{1}{5}}\)

\(a^{5} ⋅ \sqrt[8]{a^{7}} = a^{5} ⋅ a^{\frac{7}{8}} = a^{5 + \frac{7}{8}} = a^{5\frac{7}{8}}\)

\({a^{4} \over \sqrt[5]{a^{2}}} = {a^{4} \over a^{\frac{2}{5}}} = a^{4 - \frac{2}{5}} = a^{3\frac{3}{5}}\)

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

\({\sqrt[7]{x^{6}} \over \sqrt[4]{x^{3}}} = {x^{\frac{6}{7}} \over x^{\frac{3}{4}}} = x^{\frac{6}{7} - \frac{3}{4}} = x^{\frac{3}{28}}\)

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

\(\sqrt[3]{a^{9}} = a^{\frac{9}{3}} = a^{3}\)

\({p^{7} \over p^{8} ⋅ \sqrt[3]{p^{2}}} = {p^{7} \over p^{8} ⋅ p^{\frac{2}{3}}} = {p^{7} \over p^{8\frac{2}{3}}} = p^{7 - 8\frac{2}{3}} = p^{-1\frac{2}{3}}\)

\((5 a)^{-2} = 5^{-2} ⋅ a^{-2} = {1 \over 5^{2}} ⋅ {1 \over a^{2}} = {1 \over 25 a^{2}}\)

\(({1 \over 3} x)^{-2} = (3^{-1} ⋅ x)^{-2} = (3^{-1})^{-2} ⋅ x^{-2} = 3^{2} ⋅ x^{-2} = {9 \over x^{2}}\)

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

\({3 q^{3} \over 4 p^{5}}\)

\(4 a^{5\frac{5}{8}} = 4 ⋅ a^{5} ⋅ a^{\frac{5}{8}} = 4 a^{5} ⋅ \sqrt[8]{a^{5}}\)

\(\frac{5}{6} x^{-\frac{4}{7}} y^{\frac{2}{9}} = \frac{5}{6} ⋅ {1 \over x^{\frac{4}{7}}} ⋅ y^{\frac{2}{9}} = {5 ⋅ \sqrt[9]{y^{2}} \over 6 ⋅ \sqrt[7]{x^{4}}}\)