You're right, the superscript in this context means concatenation.
To prove a language isn't regular, you use the fact that any regular language can be "pumped". First, find out what "pumping" a word means (I can't do your homework for you), and then show that your language can not be pumped, and thus, can not be regular. Basically you will take a sufficiently long word that belongs to your language, and show that it cannot be broken up and pumped in such a way that it satisfies the pumping lemma.
Note that the converse of the pumping lemma is not always true: that is, if a language does NOT satisfy the pumping lemma, it may still be non-regular. For this reason, the pumping lemma is used to exclude a language from a set of languages, and not to include a language in a set of languages (such as regular). In other words, satisfying the pumping lemma is a necessary, but not sufficient, condition for a language to be regular.