5. Найдите значение выражения:

Решение:

1. а) \[ \frac{2^5 \cdot (2^3)^4}{2^{13}} = \frac{2^5 \cdot 2^{12}}{2^{13}} = \frac{2^{17}}{2^{13}} = 2^{17-13} = 2^4 = 16 \]


2. б) \[ \frac{(5^8)^2 \cdot 5^7}{5^{22}} = \frac{5^{16} \cdot 5^7}{5^{22}} = \frac{5^{23}}{5^{22}} = 5^{23-22} = 5^1 = 5 \]


3. в) \[ \frac{(2^5)^2}{2^6 \cdot 4} = \frac{2^{10}}{2^6 \cdot 2^2} = \frac{2^{10}}{2^8} = 2^{10-8} = 2^2 = 4 \]


4. г) \[ \frac{3^7 \cdot 27}{(3^4)^3} = \frac{3^7 \cdot 3^3}{3^{12}} = \frac{3^{10}}{3^{12}} = 3^{10-12} = 3^{-2} = \frac{1}{3^2} = \frac{1}{9} \]


5. д) \[ \frac{(5^2)^4 \cdot 25}{5^9} = \frac{5^8 \cdot 5^2}{5^9} = \frac{5^{10}}{5^9} = 5^{10-9} = 5^1 = 5 \]


6. е) \[ \frac{(7^3)^3 \cdot 7^2}{(7^5)^2} = \frac{7^9 \cdot 7^2}{7^{10}} = \frac{7^{11}}{7^{10}} = 7^{11-10} = 7^1 = 7 \]


7. ж) \[ \frac{3^{11} \cdot 27}{(3^4)^3 \cdot 9} = \frac{3^{11} \cdot 3^3}{3^{12} \cdot 3^2} = \frac{3^{14}}{3^{14}} = 1 \]


8. з) \[ \frac{(11^2)^3}{11^2 \cdot 11^3} = \frac{11^6}{11^5} = 11^{6-5} = 11^1 = 11 \]

Ответ: а) 16; б) 5; в) 4; г) 1/9; д) 5; е) 7; ж) 1; з) 11.