Question 1012690
there are 2 laws of exponents that are operating here.


the first is that x^a/x^b = x^(a-b)


the second is that x^-a = 1/x^a


we'll apply them both to your problem.


start with a^(1/2) / a^2.


by the first law, this becomes a^(1/2-2) which becomes a^(-3/2).


by the second law, this becomes 1/a^(3/2).


if this is correct, we can pick any value of a and we'll get the desired result.


let's let a = 4.

then 1/a^(3/2) = 1/4^(3/2) = 1/8.


now we see if that's the same as when we do a^(1/2) / a^2.


a^(1/2) = 2
a^2 = 4^2 = 16
2/16 = 1/8
same answer so we're good.