The main issue with floating point number is that it doesn't act like a ring (https://en.wikipedia.org/wiki/Ring_(mathematics) https://en.wikipedia.org/wiki/Rin

The main issue with floating point number is that it doesn't act like a ring (https://en.wikipedia.org/wiki/Ring_(mathematics) https://en.wikipedia.org/wiki/Ring_(mathematics)) because of rounding errors. For example the equality x*(y*z) = (x*y)*z doesn't hold because each multiplication introduce small rounding errors. And this kind of equations are required for the exponentiation-by-squaring method (consider for example how x**5 is computed: x**5 = (((x*x)*x)*x)*x) using a naive exponentiation approach, but also x**5 = x*(x*x)*(x*x) = x*(x*x)**2 using the exponentiation-by-squaring method). Integer operations and matrix operations are both rings, so the exponentiation-by-squaring approach works. For floating points, it doesn't give an exact result, but could still be used in practice to get an approximate result. The pow function doesn't use this approach however, because both arguments of the pow function are floating points numbers, and can thus compute things like pow(5, 0.5) = sqrt(5), or even 534.2**12.7. The exponentiation-by-squaring approach works only when the exponent is an integer, so we need other solutions. How exactly the pow function (or other math function like exp, log, cos, ...) are computed is a vast research subject in itself, but if you are interested, the Handbook of Floating-Point Arithmetic (https://perso.ens-lyon.fr/jean-michel.muller/Handbook.html https://perso.ens-lyon.fr/jean-michel.muller/Handbook.html) is both a good introduction to the domain (and the problems associated with the finite precision of floating point number), and provides a lot of techniques to work around or minimize the rounding errors that happens when manipulating floating point numbers.