What is 0 to the power of 0 equal to?

[Bailey]

simple math question. please help.

i feel kinda stupid asking this question, but what is zero to the power of zero equal to? Is it equal to zero, or one, or infinity?
or the answer will varies depending on the function since it is an indermindate power?

When i use my sci. calculator, it say error.
but, when i use a math program it say 1. And its b/c of this that I'm confuse.

 

[wubie]

http://mathforum.org/dr.math/faq/faq.0.to.0.power.html

 

[Bailey]

so...i suppose mathematician favor(or assume) the answer to be 1?
btw, thanks for the link wubie.

 

[wubie]

mmmm... I'm not so sure myself. To quote part of the article:

This means that depending on the context where 0^0 occurs, you might wish to substitute it with 1, indeterminate or undefined/nonexistent.

But is seems that there are many arguments which support 0⁰ to be equal to one.

I am sure there are some here who can provide a more informative answer than I. I just posted the link to provide an immediate answer.

Hope that it helped.

Cheers.

 

[jcsd]

This is not the first time it's come up, but this illustrates some of the problems with defining $0^0$ as $1$:

$$x^{n-1} = \frac{x^n}{x}$$

$$x^1 = x$$

$$0^0 = \frac{0}{0}$$

$\frac{0}{0}$ is indetrimnate, so to define $0^0$ as $1$ requires the (seemingly) arbitary breaking of some of the rules of algebra.

But it also came up in the other thread that sometimes there are good reasons for defining $0^0$ as [itex]1[/tex], but you'll have to ask Hurkyl about that.

 

[NateTG]

What $$0^0$$ is equal to usually depends on context. I expect that in environments where it is defined, it will usually be 1.

 

[Hurkyl]

Basically, the times when one says $0^0=1$ are the times when the operation involved really isn't about exponentiation, but about doing something repeatedly.

 

[NateTG]

Originally posted by Hurkyl
Basically, the times when one says $0^0=1$ are the times when the operation involved really isn't about exponentiation, but about doing something repeatedly.

That's not entirely correct. $0^0=1$ is also 1 if it's the base, and not the exponent that's changing.