Tricky SAT Math - Exponents

Question

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

A) 2¹²

B) 4⁴

C) 8²

D) The value cannot be determined from the information given.

Answer 1

This problem is tricky. It looks like a system of equations problem, but we have two variables and only ONE equation in the set-up, so we might assume that there isn't enough info (D).

However, we can use rules of exponents to manipulate the fraction and see something cool. We know that 8 is 2³, so we can rewrite the fraction with 2s as the bases:

8^x/2^y = (2³)^x/2^y= 2^3x/2^y

The last thing we need to do is subtract the powers and plug in the original x and y equation:

2^3x/2^y = 2^3x-y = 2¹² (A).