Why does x^0=1?

Question

or, why does x to the 0 power equal one?

Answer 1

One is the basis point for all multiplication, not zero. It doesn't seem right but it is. Something taken to itself zero times must still exist and be non-zero.

Answer 2

Assume x^0 = 0. Then The 0th root of 0 would be x for all values of x . . . at its heart this is just division by zero . . . you can prove that any number is equal to any other number. So we define x^0 so that it is consistent with the field axioms of the real number system.

Answer 3

yes, anything that has 0 power is equal to 1

Answer 4

It is a mathematical identity that any number raised to the 0 power is 1.

Answer 5

Any number raised to the power of 0 will always be 1 because there is no number to raise it up to.

Answer 6

by definition any number to the 0 power = 1. That has been defined by math people.

Answer 7

It's a basic mathematical assumption.

We know that x^0.1 = tenth root of x = number close to 1

Also, x^0.01 = hundredth root of x = number even closer to 1

And so on.

So we assume that x^a = 1 when a --> 0.

Since it fits the graph and makes the rest of math possible, even though we cannot prove it logically, we assume it to be true.

Answer 8

Easy. Since x^n * x^m = x(n+m)

x^0 = x^(n-n) = x^(n) x^(-n) = x^n / x^n = 1

Answer 9

suck it up even if you don't like it!!! And also this formula must have been devised in like 16 or 17 th Century. and all the people on the earth believe that is true so what is your basis of saying that it is not!!!!!