Question

0.00032 в степени 0.4вычислите

Answer 1

${(0.00032)}^{0.4} = ( \frac{32}{100000} ) {}^{ \frac{2}{5} } = ( \frac{1}{3125} ) {}^{ \frac{2}{5} } = \\ = \sqrt[5]{ {( \frac{1}{3125}) }^{2} } = \sqrt[5]{ (\frac{1}{ {5}^{5} }) {}^{2} } = \sqrt[5]{ {(5 {}^{ - 5} )}^{2} } = \\ = \sqrt[5]{ {5}^{ - 10} } = {5}^{ - 2} = \frac{1}{ {5}^{2} } = \frac{1}{25} = 0.04$

Answer 2

$\tt 0.00032^{0.4}=\bigg(\cfrac{32}{10^5}\bigg)^{\frac{2}{5}}=\bigg(\cfrac{2^5}{2^5\cdot5^5}\bigg)^{\frac{2}{5}}=\bigg(\cfrac{1}{5^5}\bigg)^{\frac{2}{5}}=\cfrac{1}{5^{5\cdot\frac{2}{5}}} =\cfrac{1}{5^{2}} =\cfrac{1}{25}=0.04$