# What is 0 to the power of 0?

##### 1 Answer

This is actually a matter of debate. Some mathematicians say

#### Explanation:

See the discussion on Wikipedia:

Exponentiation : Zero to the power of zero

Personally I like

Here's one argument in favour of

For any number

etc.

For any positive integer,

So what about

By analogy, that's an empty product - the product of

If we're happy with that, what about

If it's the empty product of

Unfortunately, if we look at fractional exponents, we get some nasty behaviour.

Consider

As

so you would hope

but

So exponentiation behaves badly in the neighbourhood of