465. Найдите значение выражения: 25. (23)4 a) 213; (25)2 B) 26.4 (53)4. 25 д) 59; 311.27 ж) (34)3.9; (58)2.57 37-27 (73)3.72- (113)3 б) 522; г) (34)3; e) (75)2; з) 112.113.

a) $$\frac{2^5 \cdot (2^3)^4}{2^{13}} = \frac{2^5 \cdot 2^{3 \cdot 4}}{2^{13}} = \frac{2^5 \cdot 2^{12}}{2^{13}} = \frac{2^{5+12}}{2^{13}} = \frac{2^{17}}{2^{13}} = 2^{17-13} = 2^4 = 16$$

Ответ: 16

б) $$\frac{(5^8)^2 \cdot 5^7}{5^{22}} = \frac{5^{8 \cdot 2} \cdot 5^7}{5^{22}} = \frac{5^{16} \cdot 5^7}{5^{22}} = \frac{5^{16+7}}{5^{22}} = \frac{5^{23}}{5^{22}} = 5^{23-22} = 5^1 = 5$$

Ответ: 5

в) $$\frac{(2^5)^2}{2^6 \cdot 4} = \frac{2^{5 \cdot 2}}{2^6 \cdot 2^2} = \frac{2^{10}}{2^6 \cdot 2^2} = \frac{2^{10}}{2^{6+2}} = \frac{2^{10}}{2^8} = 2^{10-8} = 2^2 = 4$$

Ответ: 4

г) $$\frac{3^7 - 27}{(3^4)^3} = \frac{3^7 - 3^3}{3^{4 \cdot 3}} = \frac{3^3(3^4 - 1)}{3^{12}} = \frac{3^3(81 - 1)}{3^{12}} = \frac{3^3 \cdot 80}{3^{12}} = \frac{80}{3^{12-3}} = \frac{80}{3^9} = \frac{80}{19683}$$

Ответ: $$\frac{80}{19683}$$

д) $$\frac{(5^3)^4 \cdot 25}{5^9} = \frac{5^{3 \cdot 4} \cdot 5^2}{5^9} = \frac{5^{12} \cdot 5^2}{5^9} = \frac{5^{12+2}}{5^9} = \frac{5^{14}}{5^9} = 5^{14-9} = 5^5 = 3125$$

Ответ: 3125

е) $$\frac{(7^3)^3 \cdot 7^2}{(7^5)^2} = \frac{7^{3 \cdot 3} \cdot 7^2}{7^{5 \cdot 2}} = \frac{7^9 \cdot 7^2}{7^{10}} = \frac{7^{9+2}}{7^{10}} = \frac{7^{11}}{7^{10}} = 7^{11-10} = 7^1 = 7$$

Ответ: 7

ж) $$\frac{3^{11} \cdot 27}{(3^4)^3 \cdot 9} = \frac{3^{11} \cdot 3^3}{3^{4 \cdot 3} \cdot 3^2} = \frac{3^{11+3}}{3^{12} \cdot 3^2} = \frac{3^{14}}{3^{12+2}} = \frac{3^{14}}{3^{14}} = 1$$

Ответ: 1

з) $$\frac{(11^3)^3}{11^2 \cdot 11^3} = \frac{11^{3 \cdot 3}}{11^2 \cdot 11^3} = \frac{11^9}{11^{2+3}} = \frac{11^9}{11^5} = 11^{9-5} = 11^4 = 14641$$

Ответ: 14641