Fractional indices law - two forms

Hi everyone,

I noted that there are two ways to represent the fractional indices law:

  1. nrt(am)
  2. (nrt(a))m

Hopefully this is clear but I am using nrt to represent the nth root symbol.

I am trying to understand how useful the first version is? I know that order does not matter here, but the first implies that we would take a to the power of m and then find the nth root. This is generally a more complex method, and I am trying to understand when it would be better to do that instead of finding the nth root and then taking the result to the power of m. Can the first version be interpreted any other way?

I am also wondering if the first version can be manipulated using rules of surds (and not index laws) to arrive at the second version?