# [Maxima] Power function: Simplification of 0^a

Dieter Kaiser drdieterkaiser at web.de
Sun Jan 17 10:26:52 CST 2010

```Am Sonntag, den 17.01.2010, 07:56 -0800 schrieb Richard Fateman:
> The arguments for value of 0^0 , at least in isolation, are presented in
> http://mathforum.org/dr.math/faq/faq.0.to.0.power.html
>
> where the value 1 is suggested.
>  Sometimes a distinction is made between 0.0^x and 0^x   and between
> types x=integer and x=real. (see link).

Yes, I know about the discussion related to the value of 0^0. But I have
not enough mathematical knowledge to decide what will be the most
convenient implementation. Therefore, I have chosen the way Maxima has
implemented this case. Maxima gives 0^0 -> undefined.

By the way: I have forgotten to mention that we have a fourth way to
implement an unknown sign. We can leave the expression 0^x unsimplified.
I have tried this too. Here are two examples:

(%i12) 0^x;
(%o12) 0^x

(%i13) hgfred([-x],[],1);
(%o13) 0^x

This works for more complex expressions too:

(%i7) (x*(0^x+1/(x-1)));
(%o7) x*(0^x+1/(x-1))

(%i8) expand(%);
(%o8) x*0^x+x/(x-1)

The testsuite will work with implementation too. Again we only get three
errors which are related to the sqrt function.

Dieter Kaiser

```