(Any Number)^0 = 1

[nycmathguy]

Let n = any number.

We know that n^(0) = 1.

Why is this the case?

 

[MathLover1]

In short, the multiplicative identity is the number 1, because for any other number x, 1*x = x. So, the reason that any number to the zero power is one is because any number to the zero power is just the product of no numbers at all, which is the multiplicative identity, 1.

 

[nycmathguy]

In short, the multiplicative identity is the number 1, because for any other number x, 1*x = x. So, the reason that any number to the zero power is one is because any number to the zero power is just the product of no numbers at all, which is the multiplicative identity, 1.

Interesting. I wonder how many students learn this stuff in high school but don't know the reason why. It is never explained.