465. Найдите значение выражения: a) $$\frac{2^5 \cdot (2^3)^4}{2^{13}}$$; б) $$\frac{(5^8)^2 \cdot 5^7}{5^{22}}$$; в) $$\frac{(2^5)^2}{2^6 \cdot 4}$$; г) $$\frac{3^7 \cdot 27}{(3^4)^3}$$; д) $$\frac{(5^2)^4 \cdot 25}{5^9}$$; e) $$\frac{(7^3)^3 \cdot 7^2}{(7^5)^2}$$; ж) $$\frac{3^{11} \cdot 27}{(3^4)^3 \cdot 9}$$; з) $$\frac{(11^2)^3}{11^2 \cdot 11^3}$$.

<p>a) $$\frac{2^5 \cdot (2^3)^4}{2^{13}} = \frac{2^5 \cdot 2^{3 \cdot 4}}{2^{13}} = \frac{2^5 \cdot 2^{12}}{2^{13}} = \frac{2^{5+12}}{2^{13}} = \frac{2^{17}}{2^{13}} = 2^{17-13} = 2^4 = 16$$</p>
<p>б) $$\frac{(5^8)^2 \cdot 5^7}{5^{22}} = \frac{5^{8 \cdot 2} \cdot 5^7}{5^{22}} = \frac{5^{16} \cdot 5^7}{5^{22}} = \frac{5^{16+7}}{5^{22}} = \frac{5^{23}}{5^{22}} = 5^{23-22} = 5^1 = 5$$</p>
<p>в) $$\frac{(2^5)^2}{2^6 \cdot 4} = \frac{2^{5 \cdot 2}}{2^6 \cdot 2^2} = \frac{2^{10}}{2^{6+2}} = \frac{2^{10}}{2^8} = 2^{10-8} = 2^2 = 4$$</p>
<p>г) $$\frac{3^7 \cdot 27}{(3^4)^3} = \frac{3^7 \cdot 3^3}{3^{4 \cdot 3}} = \frac{3^{7+3}}{3^{12}} = \frac{3^{10}}{3^{12}} = 3^{10-12} = 3^{-2} = \frac{1}{3^2} = \frac{1}{9}$$</p>
<p>д) $$\frac{(5^2)^4 \cdot 25}{5^9} = \frac{5^{2 \cdot 4} \cdot 5^2}{5^9} = \frac{5^8 \cdot 5^2}{5^9} = \frac{5^{8+2}}{5^9} = \frac{5^{10}}{5^9} = 5^{10-9} = 5^1 = 5$$</p>
<p>e) $$\frac{(7^3)^3 \cdot 7^2}{(7^5)^2} = \frac{7^{3 \cdot 3} \cdot 7^2}{7^{5 \cdot 2}} = \frac{7^9 \cdot 7^2}{7^{10}} = \frac{7^{9+2}}{7^{10}} = \frac{7^{11}}{7^{10}} = 7^{11-10} = 7^1 = 7$$</p>
<p>ж) $$\frac{3^{11} \cdot 27}{(3^4)^3 \cdot 9} = \frac{3^{11} \cdot 3^3}{3^{4 \cdot 3} \cdot 3^2} = \frac{3^{11+3}}{3^{12} \cdot 3^2} = \frac{3^{14}}{3^{12+2}} = \frac{3^{14}}{3^{14}} = 1$$</p>
<p>з) $$\frac{(11^2)^3}{11^2 \cdot 11^3} = \frac{11^{2 \cdot 3}}{11^2 \cdot 11^3} = \frac{11^6}{11^{2+3}} = \frac{11^6}{11^5} = 11^{6-5} = 11^1 = 11$$</p>
<p><strong>Ответ:</strong></p>
<ul>
<li>a) 16</li>
<li>б) 5</li>
<li>в) 4</li>
<li>г) $$\frac{1}{9}$$</li>
<li>д) 5</li>
<li>e) 7</li>
<li>ж) 1</li>
<li>з) 11</li>
</ul>