465. Найдите значение выражения: а) 2⁵·(2²)⁴/2¹³; б) (5³)²·5⁷/5²²; в) (2³)²/(2·4³); г) 3²·27/(3⁴)³; д) (3²)⁴·25/3⁸; е) (7³)³·7²/(7⁵)².

1. \(\dfrac{2^5\cdot(2^2)^4}{2^{13}}=2^{5+8-13}=2^0=1\).
2. \(\dfrac{(5^3)^2\cdot5^7}{5^{22}}=5^{6+7-22}=5^{-9}=\dfrac1{5^9}\).
3. \(\dfrac{(2^3)^2}{2\cdot4^3}=\dfrac{2^6}{2\cdot2^6}=\dfrac12\).
4. \(\dfrac{3^2\cdot27}{(3^4)^3}=\dfrac{3^2\cdot3^3}{3^{12}}=3^{-7}=\dfrac1{3^7}\).
5. \(\dfrac{(3^2)^4\cdot25}{3^8}=\dfrac{3^8\cdot25}{3^8}=25\).
6. \(\dfrac{(7^3)^3\cdot7^2}{(7^5)^2}=\dfrac{7^9\cdot7^2}{7^{10}}=7\).

Ответ: а) 1; б) \(\dfrac1{5^9}\); в) \(\dfrac12\); г) \(\dfrac1{3^7}\); д) 25; е) 7.