Какими формулами мы пользуемся?$$

$\displaystyle$  { \sqrt [n] a = a^{ \frac {1} {n} }; (a^n)^m = a^{n \cdot m} }

$2^{3-7\sqrt {2}} \cdot 8^{7\sqrt {2} \over 3} = 2^{3-7\sqrt {2}} \cdot 2^{2^{7\sqrt {2} \over 3}} = 2^{3-7\sqrt {2}} \cdot 2^{2 \cdot{7\sqrt {2} \over 3}}$$\displaystyle { a^n \cdot a^m = a^{a+m} }$

$\displaystyle{\frac{a^x}{a^y}} = a^{x-y}$

 $\displaystyle {\left( \sqrt [5] {\sqrt[3]3} \right)^{30} } = \left ( (3^ \frac{1}{3})^\frac{1}{5} \right)^{30} = 3^{ \frac{1}{3} \cdot \frac{1}{5} \cdot 30 } = 3^{ \frac{1}{15} \cdot \frac{30}{1} } = 3^2 = 9; \\ \frac {9}{90} = \frac {1}{10} =0,1$