# What does 0^0 equal?

1. Jul 15, 2010

### Null_

1. The problem statement, all variables and given/known data

It's a word problem, but I just need to simplify 0^0.

2. Relevant equations

n/a

3. The attempt at a solution

0^n = 0.
n^0 = 1.

I'm just going through a calculus book on my own this summer. It's not even a calculus question, but I've never come across this before. Which is it? 0 or 1? Why?

2. Jul 15, 2010

### Ryker

Re: 0^0

I believe it's 0 (or not even defined, such as in poles of a polynom), because from what I can remember n^0 = 1 is by definition only true for those n that are different from 0.

Last edited: Jul 15, 2010
3. Jul 15, 2010

### System

Re: 0^0

0^0 is undefined.

4. Jul 15, 2010

### skeptic2

Re: 0^0

From Wolfram Mathworld http://mathworld.wolfram.com/ExponentLaws.html

The definition 0^0=1 is sometimes used to simplify formulas, but it should be kept in mind that this equality is a definition and not a fundamental mathematical truth (Knuth 1992; Knuth 1997, p. 56).

5. Jul 15, 2010

### Null_

Re: 0^0

Okay, thanks guys. Wolfram is awesome!

6. Jul 15, 2010

### LCKurtz

Re: 0^0

Consider the binomial expansion:

$$1 = 1^2=(x+(1-x))^2 =\binom 2 0 x^0(1-x)^2+\binom 2 1 x^1(1-x) + \binom 2 2 x^2(1-x)^0$$

This doesn't work for x = 0 or 1 unless you define 00 = 1. That is an example of why it is usually defined as 1. Also why 0! = 1 in the same example.