1. (4 балла) Вычислите: 1) 32^3/5 * 64^1/2 - 125^1/3; 2) log₁₂(1/2) + log₁₂(1/72)

1. Вычисление:

1. \( 32^{\frac{3}{5}} \cdot 64^{\frac{1}{2}} - 125^{\frac{1}{3}} \)
   \( = (2^5)^{\frac{3}{5}} \cdot (8^2)^{\frac{1}{2}} - (5^3)^{\frac{1}{3}} \)
   \( = 2^3 \cdot 8^1 - 5^1 \)
   \( = 8 \cdot 8 - 5 \)
   \( = 64 - 5 \)
   \( = 59 \)
2. \( \log_{12}{\frac{1}{2}} + \log_{12}{\frac{1}{72}} \)
   \( = \log_{12}{\left( \frac{1}{2} \cdot \frac{1}{72} \right)} \)
   \( = \log_{12}{\frac{1}{144}} \)
   \( = \log_{12}{12^{-2}} \)
   \( = -2 \)

Ответ: 1) 59; 2) -2.