a^2-2a-b^2-8b+17=0
a^2-2a+1-b^2-8b+16=0
(a-1)^2+(b-4)^2=0
因为(a-1)^2>=0 (b-4)^2>=0
所以
(a-1)^2=0 即a=1
(b-4)^2=0 即b=4
a^b=1^4=1