In most cases, the answer is because the creator of the formula wanted to express it in a simple way.

eg: in F = m.a, we are defining the mass (F/a), as the property matter has to offer resistance to acceleration, when applied a particular force. In short, Newton chose to represent this model as simple as possible.

We could use a different value for m, but it would only make things more complex than they need to be.

Weird exponents start to come up when we combine previously assumed axioms, like this one. Suppose I make a new assumption based on these laws, I can no longer define what m is, so my expressions will be more complex.

In most cases, the answer is: Because the creator of the formula wanted to express it in a simple way.

E.g. in $F = ma$ we are defining the mass ($F/a$), as the property that matter has to offer resistance to acceleration when applied a particular force. In short, Newton chose to represent this model as simple as possible.

We could use a different value for $m$, but it would only make things more complex than they need to be.

Weird exponents start to come up when we combine previously assumed axioms, like this one. Suppose I make a new assumption based on these laws. I can no longer define what $m$ is, so my expressions will be more complex.