Вычислите:
1) $100^5 : 1000^2$;
2) $\frac{3^{10} * (3^{3})^5}{(3^{5})^4 * 3}$;
3) $\frac{4^{3} * 16^{2}}{2^{12}}$;
4) $\frac{45^{10}}{5^{8} * 3^{19}}$.
$100^5 : 1000^2 = (10^2)^5 : (10^3)^2 = 10^{2 * 5} : 10^{3 * 2} = 10^{10} : 10^{6} = 10^{10 - 6} = 10^{4} = 10000$
$\frac{3^{10} * (3^{3})^5}{(3^{5})^4 * 3} = \frac{3^{10} * 3^{3 * 5}}{3^{5 * 4} * 3} = \frac{3^{10} * 3^{15}}{3^{20} * 3} = \frac{3^{10 + 15}}{3^{20 + 1}} = \frac{3^{25}}{3^{21}} = \frac{3^{4}}{1} = 81$
$\frac{4^{3} * 16^{2}}{2^{12}} = \frac{(2^{2})^{3} * (2^{4})^{2}}{2^{12}} = \frac{2^{2 * 3} * 2^{4 * 2}}{2^{12}} = \frac{2^{6} * 2^{8}}{2^{12}} = \frac{2^{6 + 8}}{2^{12}} = \frac{2^{14}}{2^{12}} = \frac{2^{2}}{1} = 4$
$\frac{45^{10}}{5^{8} * 3^{19}} = \frac{(5 * 9)^{10}}{5^{8} * 3^{19}} = \frac{5^{10} * 9^{10}}{5^{8} * 3^{19}} = \frac{5^{10} * (3^2)^{10}}{5^{8} * 3^{19}} = \frac{5^{10} * 3^{2 * 10}}{5^{8} * 3^{19}} = \frac{5^{10} * 3^{20}}{5^{8} * 3^{19}} = 5^{2} * 3^{1} = 25 * 3 = 75$
Пожауйста, оцените решение
