Find the splitting field of x^(p^8)-1 over the Z/pZ.?

I know that since


(d/dx)[x^(p^8)-1]=(p^8)x^(p^8-1)=0,


because the characteristic of the field is p, the polynomial has multiple roots. But then I get stuck.Find the splitting field of x^(p^8)-1 over the Z/pZ.?
x^(p^8)-1 = (x-1)^(p^8)





so the only root is 1, so the splitting field is itself, Z/pZ