SAT Math Question Driving Me Crazy - Please Help!

<p>If a and b are positive integers and (a^1/2 x b^1/3)^6 = 432, what is the value of ab?</p>

<p>A. 6
B. 12
C. 18
D. 24
E. 36</p>

<p>This is baffling me. Every math book says you can't multiply exponents if the bases are different. So what am I supposed to do? Randomly pick numbers that are factors of the answer choices, square root and cube root them and see if any equal the 6th root of 432?? Something tells me there has to be a better way. Please, please help. Thank you!!!!!</p>

<p>well you know that a^3 x b^2 = 432</p>

<p>I would plug in a value for a which will give you a value of b.</p>

<p>For example, a = 3; b = 4</p>

<p>The answer is 12. Right?</p>

<p>Yes, it's 12. Thank you. Now it seems blindingly simple.</p>

<p>I kept trying to "solve" for ab... I guess that's not how you do it.</p>

<p>I am sure there is a more mathematical way, but why bother? :)</p>

<p>432 = 2^4 * 3^3
a^3 * b^2 = 2^4 * 3^3 =
3^3 * 4^2
a=3, b=4, ab=12.</p>