GMAT in less than a week, please help vic book page 171 bott

[wignewton]

Hello. I am working through the equations, equalities, and vics book. Page 171 on the bottom, xk^10=96(1/2)^10 (linebreak)
(3)(2^5)\(2^10)
What is the math rule that allows you to take the fraction (1/2)^10 and multiply the numerator by 2^10? I understand the part about breaking the numerator down into exponential portions, it`s the manipulation of the fractional exponent I don`t understand. I have seen this somewhere else--Can someone help me? Thanks,dan

[wignewton]

if this is the answer, please just reply yes.
96x1/2x1/2x1/2...(ten 1/2) and so it is finally 96/2 to the tenth power. thanks!

[Ben Ku]

Hi Dan,

Sorry for taking so long to get back to you. We are a bit backed up. I hope this problem didn't cause you to lose too many hairs!

I think you're referring to page 167 of the Fourth Edition of the Equations, Inequalities, and VIC Strategy Guide.

Here, we have 96 ( 1 / 2)^10. Remember (a/b)^m = (a^m)/(b^m). So in this case, we're taking (96)(1^10)/(2^10) or simply (96) / (2^10).

96 simplifies further to 3(2^5), so we have 3(2^5)/(2^10). Now if (a^n)/(a^m) = 1 / (a^(m-n), so 3(2^5)/(2^10) = 3 / (2^(10-5)) = 3 / (2^5).

Hope that helps!