Ramanujan would like it

This explanation doesn't make any sense.

With such questions, you have to be very careful with how the limit is reached. In this case, the best interpretation is that you want to find

$\lim_{n \rightarrow \infty} 1 ^n$

which is just 1.

If the question was

Given that $\lim f(x) = 1$ , $\lim g(x) = \infty$ , what is $\lim f(x) ^ { g(x) }$ ?

In such a case, the answer cannot be determined given the existing information.