设实数m,n满足m^2n^2+m^2+n^2+10mn+16=0求m^n
问题描述：
设实数m,n满足m^2n^2+m^2+n^2+10mn+16=0求m^n
答
m^2*n^2+8mn+16+m^2+n^2+2mn=0,
(mn+4)^2+(m+n)^2=0,
mn=-4,m=-n,
则当m=2时,n=-2,
当m=-2时,n=2.
当m=2,n=-2时
m^n=2^-2=1/4
当m=-2,n=2时
m^n=(-2)^2=4