Limit of $\left(1+\frac{2}{n^2}\right)^n $ 
Compute$$\lim_{n\to\infty}\left(1+\frac{2}{n^2}\right)^n $$

I dont know how to do it without using continuity of exponential function
I mean I cannot do this:
$$\lim_{x\to\infty}a_n =a  \wedge  \lim_{x\to\infty}b_n =b\Rightarrow  \lim_{x\to\infty}{a_n}^{b_n} =a^b$$ 

Hint: the expression equals $[(1+2/n^2)^{n^2}]^{1/n}.$
