Question

If 3x−y=12, what is the value of
8x/2y
?

A) 212
B) 44
C) 82
D) The value cannot be determined from the information given.

Answer 1

Answer: I think your q is for 8^x/2^y

One approach is to express

8^x /2^y

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  

8^x /2^y

gives

(2^3)^x /2^y

which can be rewritten

2^3x /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

8^x/ 2^y =212

The final answer is A.