Explanation for Question 17 From the Math (Calc) Section on the 2017 May Sat
Question 17 asks us the value of a, 2 in the equation they give us, which is X to the 24th to the 3 eighth equals X squared to the fourth. 4 Now, if you're a member from, 5 um, exponent rules, whenever we have a power taking to a higher power, 6 we multiply those powers. So essentially if we have, 7 um, eh, X to the, 8 a, to the B, that is just X to the eight 9 times B. So let's do that to both of our sides in the equation 10 that they give us to kind of have an easier thing to look at. 11 We have X, so 24 T to the a, 12 we have X 24, 13 a equals XCOR to the fourth is X to the two times four, 14 which is eight. Now, 15 if these two sides of the equation are equal, 16 and we know that because there's an equal sign, 17 we know that since the base is X on both sides, 18 that this is the same, the exponent have to be the same, 19 because if not, they wouldn't be equal to each other. 20 So we know that 24, 8 and eight have to be equal. 21 So we can kind of make another equation with that. 22 And just say, 24, 8 equals eight to solve for 23 a, all we have to do is isolate it. 24 So we divide both sides by 24, 25 and we get a equals eight over 24, 26 which if we simplify that that is just one over three or 27 B.