If (1/4)ª × 2³ = (1/2)³ª then a =

A. -3
B. -2
C. 0
D. 3
E. 4

(A) (1/4)ª × 2³ = 2 to the (3 – 2a)-th power.
(1/2)³ª = 2 to the (-3a)-th power.

Equality holds if powers are equal.
3 – 2a = -3a
a = -3
The correct answer is choice (A).
-----------

I don't understand how we are able to get the powers to have like numbers below them here. I understand that if your are able to get the variables or number the same then you can just set the powers equal but don't know how to come up with ther here. Thank you.

(1/4)ª × 2³ = (1/2)³ª

We're looking for the same base, 2.
Using properties of exponents, we can see that current bases are powers of 2:


Then we can plug in the simplified terms and use properties of exponents to arrive to the final equation form:

Take a look at the explanation above. What we do there is we use the regular properties of exponents. Take a look of how we convert (1/4)ª into 2 in the (-2a)-th power.

If something in it is unclear to you, go over the properties of exponents and try to see which ones we apply here. If you have any questions left then, fell free to ask (specifying which exact step is unclear).