3 Вычислите: 67.611 a) 615; 84.813 б) 818; 35.39 B) 312.9; г) (4/7)3. (4/7)0

1. a) $$\frac{6^7 \cdot 6^{11}}{6^{15}} = \frac{6^{7+11}}{6^{15}} = \frac{6^{18}}{6^{15}} = 6^{18-15} = 6^3 = 216$$
2. б) $$\frac{8^4 \cdot 8^{13}}{8^{18}} = \frac{8^{4+13}}{8^{18}} = \frac{8^{17}}{8^{18}} = 8^{17-18} = 8^{-1} = \frac{1}{8}$$
3. в) $$\frac{3^5 \cdot 3^9}{3^{12} \cdot 9} = \frac{3^{5+9}}{3^{12} \cdot 3^2} = \frac{3^{14}}{3^{12+2}} = \frac{3^{14}}{3^{14}} = 1$$
4. г) $$\left(\frac{4}{7}\right)^3 \cdot \left(\frac{4}{7}\right)^0 = \left(\frac{4}{7}\right)^{3+0} = \left(\frac{4}{7}\right)^3 = \frac{4^3}{7^3} = \frac{64}{343}$$

Ответ:

1. a) 216
2. б) 1/8
3. в) 1
4. г) 64/343