Transcription
Here's a good question. If 3x - y = 12, what is a x / 2 y?
Most students see two variables and immediately think, "I can't solve this. There's not enough information," and they pick d. That's the trap. The SAT doesn't want you to solve for x, and it doesn't want you to solve for y. It wants you to see the hidden structure hidden inside that fraction.
Here's our move. Because 8 is not some random number. 8 is 2 cubed. So a to the x is the same thing as 2 cubed to the power of x. Now apply the power rule. When you raise a power to a power, you multiply the exponents. 2 cubed to the x becomes 2 to the 3x.
Now your fraction is 2 to the 3x over 2 to the y. Same base on the top and bottom. When you divide same base exponentials, you subtract. So this becomes 2 to the power of 3x - y.
But look what's inside that exponent. 3x - y. And the problem told you right at the start that 3x - y = 12. So the answer is 2 to the 12th a.