Suppose I have
$$x\bigg(\frac{abcd^{n-141+xy}}{fds^{3C}}+dfd+1+... etc.\bigg)$$
In order to not have repeat the cumbersome expression within the brackets, I was wondering if there was some useful term for reference, just like how one might refer the the RHS, or LHS etc. Would the 'interior expression' make it clear what I mean?
You can call it whatever you want, it's kind of the beauty of Maths.
Yes, the "interior expression works" but the moment you operate or rearrange, you may have a new interrior expression and this may cause confusion. Your safest bet is to just "$Let$" it be anything. For example:
$Let$ $A=\bigg(\frac{abcd^{n-141+xy}}{fds^{3C}}+dfd+1+... etc.\bigg)$
Then for the rest of your work, unless you redefine $A$, you won't have to rewrite the long expression.