how (why) is m/s^2 = m x s^-2?

Answer 1

Because you can rewrite exponents in different ways:

m^-2 is the same thing as 1/m^2 (just placing the exponent in the denominator).

That's why m x s^-2 --------------> m/s^2

Answer 2

As one answer put it, these are just two different, but equivalent, ways of writing values in the denominator.

We can show they are equivalent by specifying 1/x^2 and then show it is equal to x^-2. So 1/x^2 = f(x) and f(x) x^-2 = 1 by cross multiplying. In which case x^-2 = 1/f(x) = 1/(1/x^2) = 1/x^2 QED.