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**Drexel28** You have the classic problem and the answer is...the question doesn't make sense.

Think about. This notion you have of the function $\displaystyle f(x,y)=x^y$ is only defined in terms of *real* numbers. Is $\displaystyle \infty\in\mathbb{R}$? No, so it's not a debate of "is infinity so big it makes the zeroth power go away or is the zero so small it makes the infinity go away" the answer is you really can't ask the question without introducing some new number $\displaystyle \infty$ and doing this (at least in th obvious way) screws up the algebraic structure of $\displaystyle \mathbb{R}$ ($\displaystyle \infty+1=\infty\implies 1=0$ and since this isn't true we can't additively cancel things). So, if you're asking what is $\displaystyle \lim_{x\to 0}f(x)^{g(x)}$ where $\displaystyle f\to\infty,g\to 0$ the answer is...it can be any real number you want.