Question

what is the answer to this question? I just want to double check my answer that I wrote on a test?

(3a)^1/2 x (3a)^-1/2

Answer 1

What was your answer?

Answer 2

when you multiply, you add exponents.

For example, 2^3 x 2^4 = 2^(3+4) = 2^7

Recall that negative exponents are the reciprocals of positive exponents.

2^-3 = 1/2^3 = 1/8

SO, you have

(3a)^1/2 * (3a)^-1/2
= (3a)^1/2 / (3a)^1/2 = 1

or, by adding exponents,

(3a)^1/2 * (3a)^-1/2 = (3a)^0 = 1

anything to the zeroth power is 1.

2^3/2^3 = 8/8 = 1
so, 2^(3-3) = 2^0 = 1

Answer 3

9a^-1/4

Answer 4

(3a)^2 = 9a^2
((3a)^1/2)^-1/2 = (3a)^-1/4

There's just no valid way to come up with what you got.