9: Dominant terms are 3n in the numerator and 2n in the denominator. Factoring out gives
The little fraction on the top goes to zero since exponentials beat powers, it can be proved using the l'Hospital rule (actually, just one calculation is enough, as one fraction is essentially a reciprocal of the other).
In fact, it now seems that the whole original problem could have been solved using the l'Hospital rule and it will be even easier that way. Try it.