SOLUTION: Can someone help me solve a^1/2 /a^2

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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