Treating the little-o-notation as a quantity? I understand that for two functions $f(n)$ and $g(n)$ for $n\in\mathbb N$, the notation 
$$g(n)=o(f(n)) \mbox{ as } n\rightarrow \infty$$ 
means that for all $\epsilon>0$, there exists $N\in\mathbb N$ such that $|g(n)|\le \epsilon |f(n)|$ whenever $n>N$,
or equivalently, if $f(n)$ is non-zero for sufficiently large $n$
$$\lim_{n\rightarrow \infty} \dfrac{g(n)}{f(n)}=0.$$
And variants of the notation for real functions exist too.
However, I have seen many people who treats "$o(n)$" as some quantity. For example, they write things like
$$g(n)=\left(f(n)+o\left(1/n\right)\right)^n.$$
This doesn't seem to make sense at all just looking at the definition. Can someone give me a rigorous definition of what an expression of this sort really means?

This means that $ g(n) = (f(n) + h(n))^n $ for some function $ h$ such that $h(n) = o(1/n) $.
