Часть 1 1. (4 балла) Вычислите: 1) 125^{1/3} \(\cdot\) 16^{1/4} - 9^{1/2}; 2) \(\log\)_6 18 - \(\log\)_6 3; 3) \(\frac{\sqrt[7]{256}}{\sqrt[7]{2}}\), 4) 4\(\sin\)\(\frac{\pi}{6}\) + 2\(\cos\) 2\(\pi\).

Решение:

1. 1) \( 125^{1/3} \cdot 16^{1/4} - 9^{1/2} = \sqrt[3]{125} \cdot \sqrt[4]{16} - \sqrt{9} = 5 \cdot 2 - 3 = 10 - 3 = 7 \)
2. 2) \( \log_6 18 - \log_6 3 = \log_6 \frac{18}{3} = \log_6 6 = 1 \)
3. 3) \( \frac{\sqrt[7]{256}}{\sqrt[7]{2}} = \sqrt[7]{\frac{256}{2}} = \sqrt[7]{128} = \sqrt[7]{2^7} = 2 \)
4. 4) \( 4\sin\frac{\pi}{6} + 2\cos 2\pi = 4 \cdot \frac{1}{2} + 2 \cdot 1 = 2 + 2 = 4 \)

Ответ: 1) 7; 2) 1; 3) 2; 4) 4.