Answer: One approach is to express
8x
2y
so that the numerator and denominator are expressed with the same base. Since 2 and 8 are both powers of 2, substituting 23 for 8 in the numerator of
8x
2y
gives
(23)x
2y
which can be rewritten
23x
2y
Since the numerator and denominator of have a common base, this expression can be rewritten as 2(3x−y). In the question, it states that 3x−y=12, so one can substitute 12 for the exponent, 3x−y, which means that
8x
2y
=212
The final answer is A.
