3). Вычислите: а) \(\frac{7^9 \cdot 7^{11}}{7^{18}}\); б) \(\frac{5^6 \cdot 125}{25^4}\)

a) \(\frac{7^9 \cdot 7^{11}}{7^{18}}\) = \(\frac{7^{9+11}}{7^{18}}\) = \(\frac{7^{20}}{7^{18}}\) = 7^{20-18} = 7^2 = 49\)

б) \(\frac{5^6 \cdot 125}{25^4}\) = \(\frac{5^6 \cdot 5^3}{(5^2)^4}\) = \(\frac{5^{6+3}}{5^{2 \cdot 4}}\) = \(\frac{5^9}{5^8}\) = 5^{9-8} = 5^1 = 5

Ответ: a) 49; б) 5