3) Вычислите: a) $$\frac{6^{15} \cdot 6^{11}}{6^{24}}$$; б) $$\frac{3^{11} \cdot 27}{9^6}$$.

a) $$\frac{6^{15} \cdot 6^{11}}{6^{24}} = \frac{6^{15+11}}{6^{24}} = \frac{6^{26}}{6^{24}} = 6^{26-24} = 6^2 = 36$$ Ответ: 36 б) $$\frac{3^{11} \cdot 27}{9^6} = \frac{3^{11} \cdot 3^3}{(3^2)^6} = \frac{3^{11+3}}{3^{2 \cdot 6}} = \frac{3^{14}}{3^{12}} = 3^{14-12} = 3^2 = 9$$ Ответ: 9