Reading through an old scientific paper, I've come across some potentially ambiguous notation using the del operator. In this example, $f$, $g$, and $x$ are scalars, and $\textbf{V}$ is a vector. The equation is:
$x = \nabla \cdot f \textbf{V} g.$
Should this be interpreted to indicate:
$x = \nabla \cdot \left(f g\textbf{V} \right),$
or does it possibly indicate:
$x =g \nabla \cdot \left(f \textbf{V}\right)?$
Is the answer indicated by a strict order of operations argument, or is the first form some sort of commonly known shorthand notation? I'm not sure why the two scalars would be separated if they were both intended to be part of the dot product.