x^2+y^2+xy-3y+3=0
(x^2+xy+y^2/4)+(3y^2/4-3y+3)=0
(x+y/2)^2+3(y^2/4-y+1)=0
(x+y/2)^2+3(y/2-1)^2=0
∴x+y/2=0
y/2-1=0
∴y/2=1
y=2
x=-y/2=-1
∴x^y=(-1)^2=1