Вычислите: 1) $100^5 : 1000^2$; 2) $\frac{3^{10} \cdot (3^3)^5}{(3^5)^4 \cdot 3}$; 3) $\frac{4^3 \cdot 16^2}{2^{12}}$; 4) $\frac{45^{10}}{5^8 \cdot 3^{19}}$.

Решение: 1) $100^5 : 1000^2 = (10^2)^5 : (10^3)^2 = 10^{10} : 10^6 = 10^{10-6} = 10^4 = 10000$. 2) $\frac{3^{10} \cdot (3^3)^5}{(3^5)^4 \cdot 3} = \frac{3^{10} \cdot 3^{15}}{3^{20} \cdot 3^1} = \frac{3^{10+15}}{3^{20+1}} = \frac{3^{25}}{3^{21}} = 3^{25-21} = 3^4 = 81$. 3) $\frac{4^3 \cdot 16^2}{2^{12}} = \frac{(2^2)^3 \cdot (2^4)^2}{2^{12}} = \frac{2^6 \cdot 2^8}{2^{12}} = \frac{2^{6+8}}{2^{12}} = \frac{2^{14}}{2^{12}} = 2^{14-12} = 2^2 = 4$. 4) $\frac{45^{10}}{5^8 \cdot 3^{19}} = \frac{(5 \cdot 9)^{10}}{5^8 \cdot 3^{19}} = \frac{5^{10} \cdot 9^{10}}{5^8 \cdot 3^{19}} = \frac{5^{10} \cdot (3^2)^{10}}{5^8 \cdot 3^{19}} = \frac{5^{10} \cdot 3^{20}}{5^8 \cdot 3^{19}} = 5^{10-8} \cdot 3^{20-19} = 5^2 \cdot 3^1 = 25 \cdot 3 = 75$. Ответы: 1) 10000 2) 81 3) 4 4) 75