100^1/3 * 2^8/6 * 1/5^5/3

Решите задачу:

$100^{\frac{1}{3}} \cdot 2^{\frac{8}{6}} \cdot \frac{1}{5^{\frac{5}{3}}}= 5^{2 \cdot \frac{1}{3}} \cdot 2^{2 \cdot \frac{1}{3}} \cdot 2^{\frac{4}{3}} \cdot 5^{- \frac{5}{3}}} = \\ = 5^{\frac{2}{3}} \cdot 2^{\frac{2}{3}} \cdot 2^{\frac{4}{3}} \cdot 5^{- \frac{5}{3}} =5^{\frac{2}{3} - \frac{5}{3}} \cdot 2^{\frac{2}{3}+\frac{4}{3}} = 5^{-\frac{3}{3}} \cdot 2^{\frac{6}{3}} = \\ =5^{-1} \cdot 2^{2} = \frac{4}{5} =0,8$