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

Question

I’m too dumb to get it

In: Mathematics

Answer 1

x^0 is something called an [empty product](https://en.m.wikipedia.org/wiki/Empty_product), that is, the result of multiplying zero numbers together. It is defined to be 1, the multiplicative identity (x • 1 = x), because that is the most useful and intuitive way of defining it. In any multiplication problem, let’s say (2 • 3), you can say there’s an implicit (2 • 3 • 1 • 1 • 1 • 1. . .) at the end. If you multiply zero number together, you’re left with only the (• 1 • 1 • 1 • 1. . .), so you get one.