What is the advantage of m·s^(-1) over m/s?
I think the main advantage is that an ambiguity of a/bc is avoided. For example, g/m^2s may be read as g m^{-2} s^{-1} or g m^{-2} s depending on whether multiplication takes priority over division.  As far as I know, there is no consistency in opinions about it, so to avoid confusion a slightly uglier notation with negative powers may be worth accepting.