(3×2 ​^−2 ​​ ) ​^−2 Give a simplified form and numeric answer to this

Question

I need help trying to figure out this answer.

Answer 1

In the order of operations, we do the 2^-2 first. This can be expressed as the reciprocal of the positive exponent, therefore 1 / 2^2. Since this equals 1/4, the quantity within the parentheses is 3 x 1/4, or 3/4.

Now we would do the same operation on the (3/4)^-2 by using the reciprocal again.

1 1 1 16

-------------- = --------------- = ------------- = ---------

(3/4)^2 3/4 x 3/4 9/16 9

So 16/9 is the answer, or reducing, 1 7/9 (one and seven ninths).