0**0 is undefined according to wikipedia, but 1 is clearly the limit of x**0 as x tends to 0 from above. Limit points are usually left in that form (i.e. as the limit of a Cauchy sequence) or reused in that form (hence the need for something like l'Hopital to take you further) - this being preferable than risking error by trying to reuse the expression in a determinate way.

However, what might be "undefined" in a mathematical sense is rather a different idea from being undefined in Perl. Leaving $x undefined after $x = 0**0 isn't reasonable. The only reasonable choices seem to be to return an error or attempt a defined assignment - Perl cannot (yet?) do the ideal(?) thing of leaving it defined as "the limit of x^0 as x tends to 0 from above" and that wouldn't really be useful either!