Indeterminate Form Discussion - 1^(inf)

In my AP Calculus class, we had a lengthy discussion regarding the indeterminate form Attachment 26414. Other bases to infinity either turn out to be infinity itself or 0, depending on the base. To me, that doesn't make sense. Why are quantities, such as Attachment 26415, are determinate, but Attachment 26414 is not? Just want to hear some opinions.

Dr. Math discusses why ...

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1^Infinity is and indeterminate fore because infinity is not a real number. There are no rules for how exponentiation works on something that isn't a number. Plus x=1^infinity is like you are saying infinity*ln(1) which doesn't exist.