10: Changing the product into a ratio gives
As expected, this is an indeterminate ratio, no tricky way out seems possible, so apply the l'Hospital rule.
Remark: If you tried to do the logarithm separately, you should get
So this way it is indeed shorter, because you got lucky.
However, if you try to handle the power separately, it won't work:
Note that it was not necessary to compute past the third line. By the scale of powers, powers beat logarithms, so it is clear right away that the second limit is zero and one gets an indetermiante product. This is a blind alley.