Question 1012690: Can someone help me solve a^1/2 /a^2
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! 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.
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