3. Вычислите: a) \(\frac{6^5}{6^2} \cdot \frac{6^{12}}{6^{11}}\) б) \(\frac{2^5 \cdot 5^4}{5^2 \cdot 2^3}\)

Решение:

a) \(\frac{6^5}{6^2} \cdot \frac{6^{12}}{6^{11}} = 6^{5-2} \cdot 6^{12-11} = 6^3 \cdot 6^1 = 6^{3+1} = 6^4\)

б) \(\frac{2^5 \cdot 5^4}{5^2 \cdot 2^3} = \frac{2^5}{2^3} \cdot \frac{5^4}{5^2} = 2^{5-3} \cdot 5^{4-2} = 2^2 \cdot 5^2 = (2 \cdot 5)^2 = 10^2 = 100\)

Ответ: а) \(6^4\); б) 100.