64c²d⁴-4n⁶=(8cd²)²-(2c³)²=(8cd²+2c³)(8cd²-2c³).
Вот решение:
3a/4c -(9a²+16c²)/12ac+(4c-9a)/3a = (9a²-9a²-16c²+16c²-36ac)/12ac =
= -36ac/12ac = -3
Ответ: -3
![\frac{(25^{n}-5^{2n-2})^{ \frac{1}{2}} }{(125^{n-1}-61*5^{3n-6})^{ \frac{1}{3} }}= \frac{(5^{2n}-5^{2n-2})^{ \frac{1}{2} }}{(5^{3n-3}-61*5^{3n-6})^{ \frac{1}{3} }}= \frac{ \sqrt{5^{2n}(1-5^{-2})} }{ \sqrt[3]{5^{3n-3}(1-61*5^{-3})} }=\\\\= \frac{5^n(1- \frac{1}{25}) }{5^{n-1}(1- \frac{61}{125}) }= \frac{5^n\sqrt{ \frac{25-1}{25}} }{5^{n-1} \sqrt[3]{ \frac{125-61}{125} } }= \frac{5^{n-n+1}\sqrt{ \frac{24}{25}} }{\sqrt[3]{ \frac{64}{125} } } =\\\\= \frac{5* \frac{ 2\sqrt{6} }{5} }{ \frac{4}{5} }=](https://tex.z-dn.net/?f=%20%5Cfrac%7B%2825%5E%7Bn%7D-5%5E%7B2n-2%7D%29%5E%7B%20%5Cfrac%7B1%7D%7B2%7D%7D%20%7D%7B%28125%5E%7Bn-1%7D-61%2A5%5E%7B3n-6%7D%29%5E%7B%20%5Cfrac%7B1%7D%7B3%7D%20%7D%7D%3D%20%20%5Cfrac%7B%285%5E%7B2n%7D-5%5E%7B2n-2%7D%29%5E%7B%20%5Cfrac%7B1%7D%7B2%7D%20%7D%7D%7B%285%5E%7B3n-3%7D-61%2A5%5E%7B3n-6%7D%29%5E%7B%20%5Cfrac%7B1%7D%7B3%7D%20%7D%7D%3D%20%5Cfrac%7B%20%5Csqrt%7B5%5E%7B2n%7D%281-5%5E%7B-2%7D%29%7D%20%7D%7B%20%5Csqrt%5B3%5D%7B5%5E%7B3n-3%7D%281-61%2A5%5E%7B-3%7D%29%7D%20%7D%3D%5C%5C%5C%5C%3D%20%5Cfrac%7B5%5En%281-%20%5Cfrac%7B1%7D%7B25%7D%29%20%7D%7B5%5E%7Bn-1%7D%281-%20%5Cfrac%7B61%7D%7B125%7D%29%20%7D%3D%20%5Cfrac%7B5%5En%5Csqrt%7B%20%5Cfrac%7B25-1%7D%7B25%7D%7D%20%7D%7B5%5E%7Bn-1%7D%20%5Csqrt%5B3%5D%7B%20%5Cfrac%7B125-61%7D%7B125%7D%20%7D%20%7D%3D%20%20%5Cfrac%7B5%5E%7Bn-n%2B1%7D%5Csqrt%7B%20%5Cfrac%7B24%7D%7B25%7D%7D%20%7D%7B%5Csqrt%5B3%5D%7B%20%5Cfrac%7B64%7D%7B125%7D%20%7D%20%7D%20%3D%5C%5C%5C%5C%3D%20%5Cfrac%7B5%2A%20%5Cfrac%7B%202%5Csqrt%7B6%7D%20%7D%7B5%7D%20%20%7D%7B%20%5Cfrac%7B4%7D%7B5%7D%20%7D%3D)
=2,5√6
В ответе не содержится переменная n, следовательно, значение выражения не зависит от n
1)5^3*2^3=125*8=1000
2)(1/4)^4*20^4=1/256*160000=625
3)(0.5)^3*60^3=0.125*216000=27000
4)(1.2)^4*(1 2/3)^4=2.0736*625/81=16