Let $W=X/Y$ be a quotient of $X$
Let $W/Z$ be a quotient of $W$
To write $W/Z$ without $W$, Would we need to write $(X/Y)/Z$? I presume $X/Y/Z$ is ambiguous?
I'm imagining a group quotient and not assuming this is necessarily the same or different for other types of quotient.
Yes, one would write $(X/Y)/Z$.
However, note that this implies that $Z$ is a normal subgroup of $W$, and thus since $W$ is a quotient group of $X$ we may identify $Z = \pi(K)$ where $K$ is a normal subgroup of $X$, $Y \subseteq K$, $\pi: X \rightarrow X/Y = W$ is the canonical projection. Then by the third iso theorem we have
$$(X/Y) /Z = (X/Y)/(K/Y) = X/K ~~.$$