eli5: Why is x^0=1?

Question

I’m confused, shouldn’t it be 0?

In: Mathematics

Answer 1

Suppose you want to solve x^y=z to find y. You can think of that as asking how many times you have to multiply 1 by x to get z.

So for instance with 2^y =8. You have to multiply 1 by 2 three times to get eight: 1x2x2x2 = 8.

So how many times do you have to multiply 1 by anything to get 1? The answer is zero times – it’s already 1.