can someone explain this:

Question

how is having a square in the denominator equivalent to taking the reciprocal and raising it to the 1/2 power?

EX:

here's an identity:

let x= 1/(2a^2)
a = M/2RT

so can this be rewritten as: (1/2)(2RT/M)^(1/2)

Answer 1

It's not.
Having a square root is.

√x = x^(1/2)
1/√x = x^(-1/2)

Your assertion is true if you are solving for a, since to find a you need to take the square root.