Negatieve en gebroken exponenten

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

\({7 x^{3} \over 9 x^{4}} = {7 \over 9} ⋅ {x^{3} \over x^{4}} = {7 \over 9} ⋅ x^{3 - 4} = {7 \over 9} x^{-1}\)

\({x^{4} \over x^{-8}} = x^{4 - -8} = x^{12}\)

\({({1 \over p^{8}}) \over p^{4}} = {p^{-8} \over p^{4}} = p^{-8 - 4} = p^{-12}\)

\({p^{3} \over ({1 \over p^{8}})} = {p^{3} \over p^{-8}} = p^{3 - -8} = p^{11}\)

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

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

\((a^{3})^{-6} = a^{3 ⋅ -6} = a^{-18}\)

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

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

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

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

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

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

\({\sqrt[8]{x^{7}} \over \sqrt[9]{x^{5}}} = {x^{\frac{7}{8}} \over x^{\frac{5}{9}}} = x^{\frac{7}{8} - \frac{5}{9}} = x^{\frac{23}{72}}\)

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

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

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

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

\(({1 \over 2} p)^{-5} = (2^{-1} ⋅ p)^{-5} = (2^{-1})^{-5} ⋅ p^{-5} = 2^{5} ⋅ p^{-5} = {32 \over p^{5}}\)

\({4 \over x^{8}}\)

\({2 y^{6} \over 7 x^{3}}\)

\(2 a^{6\frac{2}{3}} = 2 ⋅ a^{6} ⋅ a^{\frac{2}{3}} = 2 a^{6} ⋅ \sqrt[3]{a^{2}}\)

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