Вариант II 1. Вычислить: 1) 29.16.80 44.25 1 ; 2) (3√81)2.

1. Вычислить:

1)

$$ \frac{2^9 \cdot 16 \cdot 8^0}{4^{\frac{1}{5}} \cdot 2^5} $$ $$ = \frac{2^9 \cdot 2^4 \cdot 1}{2^{\frac{2}{5}} \cdot 2^5} $$ $$ = \frac{2^{13}}{2^{\frac{2}{5}+5}} $$ $$ = \frac{2^{13}}{2^{\frac{27}{5}}} $$ $$ = 2^{13-\frac{27}{5}} $$ $$ = 2^{\frac{65-27}{5}} $$ $$ = 2^{\frac{38}{5}} $$

2)

$$ (3\sqrt[3]{81})^2 $$ $$ = (3\sqrt[3]{3^4})^2 $$ $$ = (3 \cdot 3^{\frac{4}{3}})^2 $$ $$ = (3^{\frac{3}{3}} \cdot 3^{\frac{4}{3}})^2 $$ $$ = (3^{\frac{7}{3}})^2 $$ $$ = 3^{\frac{14}{3}} $$ $$ = 3^{4\frac{2}{3}} $$

Ответ: 1) $$2^{\frac{38}{5}}$$; 2) $$3^{\frac{14}{3}}$$.