1. (4 балла) Вычислите: 1) 125^(1/3) * 16^(1/4) - 9^(1/2); 2) log6(18) - log6(3); 3) (sqrt(256))/(sqrt(2)); 4) 4sin(pi/6) + 2cos(2pi).

Решение:

1. \( 125^{\frac{1}{3}} \cdot 16^{\frac{1}{4}} - 9^{\frac{1}{2}} = \sqrt[3]{125} \cdot \sqrt[4]{16} - \sqrt{9} = 5 \cdot 2 - 3 = 10 - 3 = 7 \)
2. \( \log_6{18} - \log_6{3} = \log_6{\frac{18}{3}} = \log_6{6} = 1 \)
3. \( \frac{\sqrt[3]{256}}{\sqrt[3]{2}} = \sqrt[3]{\frac{256}{2}} = \sqrt[3]{128} = \sqrt[3]{64 \cdot 2} = 4\sqrt[3]{2} \)
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) 4\(\sqrt[3]{2}\); 4) 4.