I actually referred to a different pattern to help knowing what x^0 is above. Not from calc, but just a different way than yours. If you start with x^3, x^2, x^1, x^0, x^-1, x^-2, and expand the forms, you get xxx, xx, x, ... where the pattern is each step divides by x. So x/x = 1 is the next, and 1/x is the next, and 1/xx is the next, ...