1. (4 балла) Вычислите: 1). 36^1/2 * 125^(1/3) - 8^(2/3); 2) log_3 8 - log_3 24; 3) 3*sqrt(3)/sqrt(625); 4) 2sin(pi/6) + 4cos(pi/2).

Решение:

1. \( 36^{1/2} \cdot 125^{1/3} - 8^{2/3} = \sqrt{36} \cdot \sqrt[3]{125} - (\sqrt[3]{8})^2 = 6 \cdot 5 - 2^2 = 30 - 4 = 26 \)
2. \( \log_3 8 - \log_3 24 = \log_3 \frac{8}{24} = \log_3 \frac{1}{3} = -1 \)
3. \( \frac{\sqrt[3]{3}}{\sqrt[3]{625}} = \sqrt[3]{\frac{3}{625}} \)
4. \( 2\sin{\frac{\pi}{6}} + 4\cos{\frac{\pi}{2}} = 2 \cdot \frac{1}{2} + 4 \cdot 0 = 1 \)

Ответ: 1) 26; 2) -1; 3) \( \sqrt[3]{\frac{3}{625}} \); 4) 1.