Why every number to the power of 0 is equal to 1?

Question

I’m too dumb to get it

In: Mathematics

Answer 1

There were better explenations here but here is another angle. You can also look at it in terms of an empty product.

If you look at an empty sum, then it should be the neutral element for addition, so 0. (Add 0 to any number and it stays the same). So if add up a number 0 times to it self, it’s 0. Look at 0*x = 0 for any number x.

By the same logic an empty product should be the neutral element of multiplication, so 1. (Multiply any number with 1 and it stays the same). So if you multiply a number 0 times by it self, It’s 1. Look at x^0 = 1 for any number x.