this was an actual hard problem on the SAT...

If 3x-y=12; find 8^x/2^y. The answer is 2^12. The answer lies in the question itself.

In the equation, we have

3x - y = 12.

This means 3x = 12 + y.

We have to find 8^x/2^y.

8 can be written as 2^3. Therefore, 8^x = 2^3x.

But 3x = 12 + y, hence can be replaced.

Now we have, in the fraction, 2^(12 + y)/2^y.

This can be written as 2^(12 + y - y) = 2^12.

Besides, I looked this up.

this is how my math teacher solved this problem:
given 8^x/2^y.
based on the power rule of exponents, 8^x can be rewritten as 2^3x.
you get 2^3x/2^y.
the use the quotient rule of exponents, if bases are equal then when exponents divide, they subtract.
you get 2^3x-y.
since you know 3x-y is 12, you can plug 12 into 3x-y which gives you 2^12.
therefore, A is the correct answer.

that is correct

sorry but that's not the right answer

K