Is 2 raised to the power of infinity=infinity?

As others have stated, infinity isn't a number, so you can't carry out mathematical operation with it in any normal sense. [ You can take limits, however, and that why infinity and zero are the normal answers to your question.
Here's something for you to ponder. If you have a set S of n elements, the number of subsets of set S is 2^n. So how many subsets are there of the set of natural numbers N, {0,1,2,3...}? That would be one answer to your question of what's 2^infinity.
Mathematicians have assigned names to these "transfinite numbers: and say that there are "aleph-null" natural numbers

("countably infinite), but that the cardinality of the set of real numbers (cardinality of the continuum) is 2^{aleph-null}= aleph-one. This is greater than aleph-null since the real numbers are "uncountable": they can't be put into 1-1 correspondence with the natural numbers. So mathematicians distinguish between different orders of infinity.
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Expert answered|sharpies|Points 7218|

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Asked 3/31/2012 1:16:30 PM

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