1. (4 балла) Вычислите: 1) 36^{1/2} \(\cdot\) 125^{1/3} - 8^{2/3}; 2) \(\log\)_3 8 - \(\log\)_3 24; 3) \(\frac{\sqrt[3]{5}}{\sqrt[3]{625}}\); 4) 2\(\sin\)\(\frac{\pi}{6}\) + 4\(\cos\)\(\frac{\pi}{2}\).

Решение:

1. 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. 2) \( \log_3 8 - \log_3 24 = \log_3 \frac{8}{24} = \log_3 \frac{1}{3} = -1 \)

3. 3) \( \frac{\sqrt[3]{5}}{\sqrt[3]{625}} = \sqrt[3]{\frac{5}{625}} = \sqrt[3]{\frac{1}{125}} = \frac{1}{5} \)

4. 4) \( 2\sin\frac{\pi}{6} + 4\cos\frac{\pi}{2} = 2 \cdot \frac{1}{2} + 4 \cdot 0 = 1 + 0 = 1 \)

Ответ: 1) 26; 2) -1; 3) 1/5; 4) 1.