题目

若x^2m=3,y^3n=2,求(x^3m)^2+(y^n)^3-x^my^4nx^3my^5n的值.

提问时间：2021-03-09

答案

x^2m=3 => x^m = 3^(1/2)
y^3n=2 => y^n=2^(1/3)
(x^3m)^2+(y^n)^3-x^my^4nx^3my^5n
=x^6m + y^3n - x^my^4nx^3my^5n
= (x^m)^6 + (y^n)^3 - (x^m)(y^n)^4 * (x^m)^3 * (y^n)^5
= [3^(1/2)]^6 + [2^(1/3)]^3 - 3^(1/2)* [2^(1/3)]^4 * [3^(1/2)]^3 * [2^(1/3)]^5
=3^3 + 3 - 3^(1/2)* [2^(4/3)] * [3^(3/2)] * [2^(5/3)]
= 9 + 3 - 3^2 * 2^3
= 9+ 3-6*6
= -24