The uncertainty principles are inequalities, not equations. And that is something you can write with multiple forms.

As for equations, notice that many equations in Physics have a constant which turns a proportion to an equation. This is where you have leeway in constructing more or less arbitrary equations based on the variables you think are important enough to observe.

Coming to your example, Newton's f = ma equation is really f/m proportional to a. The units are chosen carefully to make the constant 1. This works under the assumption that mass is constant and acceleration is measured measured from a non accelerating frame of reference with non relativistic speeds. So, yes there are several other ways to write that equation.