Why is any number to the power of 0 = 1?

X^a / X^b = X^(a - b)

When a = b then a - b = 0

But that means that X^a / X^b = X^a / X^a, which is one.

x^3 = 1 * x * x * x
x^2 = 1 * x * x
x^1 = 1 * x
x^0 = 1

∴ x^0 = 1

What happens is that you are dividing that number by itself. Any number divided by itself is 1. Don't confuse this by multiplying a number by zero. Any number multiplied by zero will equal zero.

x>a/x>b = x >(a-b), let a=b you will have x>a>/x>a =x >(a-a) =x>0= 1 This happens every time

A^m/A^m=1^m=A^0=1

agree with the friend above.

Because of the law of exponents.

1= 3^4/3^4=3^(4-4)=3^0

It isn't!

It's not. Zero to whatever power will always be zero.