If 3x−y=12, what is the value of 8x2y?
a) 212
b) 44
c) 82
d) the value cannot be determined from the information given.

One approach is to express

8x2y

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 8x2y gives

(23)x2y

which can be rewritten

23x2y

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

8x2y=212

The final answer is A.

Step-by-step explanation:

The answer is A.