If I want to express "the product of $2n$ factorial and $3n$ factorial," is it clear enough to write $2n!3n!$, or is it necessary (or preferable) to write $(2n)!(3n)!$ for clarity?
The reason I ask is that there were no parentheses in the first expression on this question but no one seemed bothered. Maybe the need for parentheses is context-dependent?
The precedence of factorial is higher than of multiplication, thus
$$an! \neq (an)!$$