Вычислите: (625^(-1/3)·5)/(25^1/3).

Ответ:

\[\frac{625^{- \frac{1}{3}} \cdot 5}{25^{\frac{1}{3}}} = \frac{\left( 5^{4} \right)^{- \frac{1}{3}} \cdot 5}{\left( 5^{2} \right)^{\frac{1}{3}}} = \frac{5^{- \frac{4}{3}} \cdot 5}{5^{\frac{2}{3}}} =\]

\[= 5^{- \frac{1}{3}}\ :5^{\frac{2}{3}} = 5^{- \frac{3}{3}} = 5^{- 1} = \frac{1}{5}.\]