5. Вычислите: 1) $$\frac{4^6 \cdot 2^9}{32^4}$$; 2) $$(\frac{2}{3})^5 \cdot (\frac{3}{8})^6$$

1) $$\frac{4^6 \cdot 2^9}{32^4} = \frac{(2^2)^6 \cdot 2^9}{(2^5)^4} = \frac{2^{12} \cdot 2^9}{2^{20}} = \frac{2^{12+9}}{2^{20}} = \frac{2^{21}}{2^{20}} = 2^{21-20} = \mathbf{2^1 = 2}$$ 2) $$(\frac{2}{3})^5 \cdot (\frac{3}{8})^6 = \frac{2^5}{3^5} \cdot \frac{3^6}{8^6} = \frac{2^5}{3^5} \cdot \frac{3^6}{(2^3)^6} = \frac{2^5 \cdot 3^6}{3^5 \cdot 2^{18}} = \frac{3^{6-5}}{2^{18-5}} = \frac{3^1}{2^{13}} = \mathbf{\frac{3}{8192}}$$