why X⁰ is equal to 1

Question

X² is X times X.
X¹ is X.
In X^Y Y is the factor that decides how many Xs are getting multiplied.

So why is X⁰ 1? It comes out of nowhere. Zero Xs are getting multiplied, so there’s no numbers being multiplied, meaning there’s nothing.

In: Mathematics

Answer 1

Here’s another way to look at the multiplication rule

x^3 = 1 * x * x * x

x^2 = 1 * x * x

x^1 = 1 * x

x^0 = 1

If that seems arbitrary, here’s another explanation. When divide x^y by x, you get x^y-1 . So x^3 / x is x^2, x^2 / x is x. So when you divide x^1 / x, you get x^0 . But x^1 / x, is just 1, so x^0 = 1