Why do we need to raise the whole pi_3 to power of -1/2?

[hotjohn]

Homework Statement

in the third photo attached , why do we need to raise the whole pi _3 to power of -1/2 ?
can we do so ? if we do so , the original pi_3 will be changed , right ?

Homework Equations

The Attempt at a Solution

 

[fresh_42]

That's impossible to read and maybe a little long. Could you type in a more condensed question in latex?

 

[haruspex]

I can't read the attachments either, much too fuzzy.
But maybe I can answer the question. The basic idea is to find dimensionless terms (the 'pi' terms) formed by raising the parameters to various powers and multiplying them together. There is 1 degree if freedom in each such term. E.g. If you came up with m¹l¹F^-1t^-2, you could equally write it as m²l²F^-2t^-4. That combines the same parameters in the same ratios, so is still dimensionless, and represents the same mixture.
Does that explain it?