先化简,再求值：[-xy/(x-y)^2]^4*(x^2-xy/x)3*x^4/y^10÷(x/xy-y^2)^5

题目

先化简,再求值：[-xy/(x-y)^2]^4*(x^2-xy/x)3*x^4/y^10÷(x/xy-y^2)^5
先化简,再求值：[-(xy)/(x-y)^2]^4*(x^2-xy/x)3*x^4/y^10÷(x/xy-y^2)^5,其中x=-2,y=4.

答案

[-(xy)/(x-y)^2]^4*[(x^2-xy)/x]^3*x^4/y^10÷[x/(xy-y^2)]^5
=(x^4y^4)/(x-y)^8*(x-y)^3*x^4/y^10*[y^5(x-y)^5]/x^5
=x^3/y
代入x=-2,y=4,
原式=(-2)^3/4=-2.