Why x^0 = 1.

To get from x^4 to x^5. You have to multipy by x. To go down 1, you divide by x. You would go from x^5 to x^4.

x^1 is x. Now to go down 1 we have to do the same thing above, divide by x.

x divided by x is 1. x^1 is the same as x. That's why x^0 = 1.