<p>ok, math is my best subject, and i usually don't have any trouble doing the problems, but there is one question i can't figure out for the life of me:</p>
<p>if a and b are positive integers and (a^(1/2) x b^(1/3))^6 = 432, what is the value of ab?? (so a to the 1/2 times b to the 1/3 all to the 6th power equals 432)
answer: ab=12</p>
<p>the ONLY way i can figure this out is by plugging numbers in, but i know there must be some algebraic way to do it
PLEASE HELP!!</p>
<p>hmm, this one is very tricky.
from the orig equ., you can see that (a^3)(b^2) = 432
i'm not sure how you can figure it out algebraically from here.. sorry</p>
<p>a=cubic root(432/b^2)
plug this value of a (which is in function of b) into the original equation. U will find a value for b. Take that value and plug it in the equation again to find a. Time a by b. </p>
<p>A little long, but that's what I can thind of now.</p>
<p>Once you get from (a^(1/2) x b^(1/3))^6 = 432 to (a^3)(b^2) = 432, then you need to factor 432
432 = 2 * 216 = 2^2 * 108 = 2^3 * 54 = 2^4 * 27 = 2^4 * 3^3.
Now, you need to make this fit the for (a^3)(b^2), so 2^4 * 3^3 = 4^2 * 3^3, so a = 3 and b = 2, meaning ab = 6</p>
<p>I have a feeling this is a blue book problem - if so, check out the consolidated solutions thread for past posts about this question</p>
<p>b^2 * a^3
4^2 * 3^3
a=3, b=4
ab=12</p>
<p>Whoops.. pike is right.. a = 3 and b = 4, not 2 so ab=12</p>
<p>thank you everyone for your help; i would have never thought to factor it. honestly the last time i did any sort of factoring was like 7th grade....</p>