Simplify negative powers of ComplexInfinity?

Questions
,
1

Hello!

When using Mathematica 9, I encounter the following problem:

Assuming[p == -1, ComplexInfinity^p]

Infinity::indet: Indeterminate expression ComplexInfinity^p encountered. >>

but

ComplexInfinity^(-1)

0

Is there any way I can tell Mathematica to evaluate ComplexInfinity^p as 0 when assuming p<0? The same problem also arises in FullSimplify, for example when considering the generalized mean of 0 and 2,

FullSimplify[(0^p + 2^p)^(1/p), p < 0]

Indeterminate

Any suggestions would be much appreciated.

2

What about taking a limit?

In[9]:= FullSimplify[(x^p + 2^p)^(1/p), p < 0]
Out[9]= (2 x)/(2 + x)

In[10]:= Limit[FullSimplify[(x^p + 2^p)^(1/p), p < 0], x -> 0]
Out[10]= 0