[Video] Q14: If 3x - y = 12, what is the value of 8^x/2^y

Explanation for Question 14 From the Math (No Calc) Section on the Official Sat Practice Test 1

So question number 14 is asking us what is eight to the X over 2 two to the lie. And so you might be tempted to go ahead and 3 do four to the X minus Y you might be tempted to divide these 4 and then subtract the exponents. Cause you know, the exponent rule that you subtract 5 the exponents when you're dividing, but that rule only comes into play when you're 6 working from the same base. And here, 7 our bases are different. One of our basis is eight and the other basis 8 too. So our goal should be to create this expression so that both of 9 the bases are two. And we can do this first by rewriting 10 this eight. We know that eight is also equal to two to the third, 11 right? Because two times two times two is eight. 12 So I can rewrite this as this expression as two to the third, 13 to the X, over two to the Y just by replacing the eight X. 14 Now we can remember from our exponent rules that when I have a parentheses, 15 I can multiply these exponent. So what I really have is two to the 16 three X over two to the Y. So now that I have the same 17 base on both my numerator and denominator, 18 both of the bases are two. I can do my exponent rule where I 19 subtract exponents. So I'll rewrite it. 20 It's two. It's not going to be one because you don't actually divide the 21 numbers. When you're doing the exponents. 22 You just take the number as it is two to the three X minus 23 Y. Now, earlier in the problem, 24 we were told that three X minus Y is equal to 12. 25 So this is also equal to 12. And that would mean that two to 26 the 12th is also equal to our expression up here. 27 So a is going to be our best answer.