Understanding the Need to Change π3 to π3' in Buckingham Theorem

[welovephysics]

Homework Statement

why there is a need to change π3 to π3 ' (which is inverse of reynold number)? (in 2nd picture)

Homework Equations

The Attempt at a Solution

why can we do so ? i was told that π1 = f( π2 , π3 , ...)
if we use π3' , which is this will change the original meaning of π1 = f( π2 , π3 , ...) , am i right ? IMO, this is wrong , there's no need to change π1 = f( π2 , π3 , ...) 3 to π1 = f( π2 , π3 , ...) 3 ' ...
can someone explain on it ? [/B]

 

[haruspex]

If π1 is a function of π2 and π3 then it is also true that it is a function of π2 and π3^-1. It's just a different function.
Until you have locked in how f is defined, you are free to choose how to define it.
That said, I don't see the advantage here in switching from π3 to π3^-1.