Our variable, , is in the exponent. That's going to be tricky to deal with. One general strategy in this situation is to use logarithms to rewrite the expression so that the variable is no longer in the exponent (recall that ).

Okay, so let's assume that the limit does exist, and that approaches some finite number. Let's call this number . Then we have

.

Taking the natural logarithm of both sides gives us

.

And since is continuous (for positive ), we are allowed to bring it inside:

.

(from the above property of logarithms)

.

Now our limit produces the indeterminate form , so we may apply L'Hôpital's rule. Then we get

.

We have therefore demonstrated that .