1. (4 балла) Вычислите: 1) 36^{1/2} · 125^{1/3} - 8^{1/3}; 2) log_3 8 - log_3 24; 3) ³√5 / ³√625; 4) 2sin(π/6) + 4cos(π/2).

Решение:

1. \( 36^{1/2} · 125^{1/3} - 8^{1/3} = \sqrt{36} · ³√{125} - ³√{8} = 6 · 5 - 2 = 30 - 2 = 28 \)
2. \( \log_3 8 - \log_3 24 = \log_3 \frac{8}{24} = \log_3 \frac{1}{3} = -1 \)
3. \( ³√{5} / ³√{625} = ³√{\frac{5}{625}} = ³√{\frac{1}{125}} = ³√{\frac{1}{5^3}} = \frac{1}{5} \)
4. \( 2\sin(\frac{\pi}{6}) + 4\cos(\frac{\pi}{2}) = 2 · \frac{1}{2} + 4 · 0 = 1 + 0 = 1 \)

Ответ: 1) 28; 2) -1; 3) 1/5; 4) 1.