4. Вычислите: a) \(\frac{32^2 \cdot 2^5}{2^{12}}\) б) \(\frac{3^5 \cdot 4^5}{12^3}\)

4. Вычисляем:
a) (\(\frac{32^2 \cdot 2^5}{2^{12}}\) = \(\frac{(2^5)^2 \cdot 2^5}{2^{12}}\) = \(\frac{2^{10} \cdot 2^5}{2^{12}}\) = \(\frac{2^{15}}{2^{12}}\) = 2^{15-12} = 2^3 = 8)
б) (\(\frac{3^5 \cdot 4^5}{12^3}\) = \(\frac{3^5 \cdot (2^2)^5}\){\(3 \cdot 4\)^3} = \(\frac{3^5 \cdot 2^{10}}{3^3 \cdot 4^3}\) = \(\frac{3^5 \cdot 2^{10}}{3^3 \cdot (2^2)^3}\) = \(\frac{3^5 \cdot 2^{10}}{3^3 \cdot 2^6}\) = 3^{5-3} \(\cdot\) 2^{10-6} = 3^2 \(\cdot\) 2^4 = 9 \(\cdot\) 16 = 144)