Welcome to College Confidential!

The leading college-bound community on the web

Sign Up For Free

Join for FREE, and start talking with other members, weighing in on community discussions, and more.

Also, by registering and logging in you'll see fewer ads and pesky welcome messages (like this one!)

As a CC member, you can:

  • Reply to threads, and start your own.
  • Post reviews of your campus visits.
  • Find hundreds of pages of informative articles.
  • Search from over 3 million scholarships.

Blue book math question

PencilxBoxesPencilxBoxes Registered User Posts: 305 Junior Member
edited May 2011 in SAT Preparation
It's on pg 714, #8. (New blue book btw)

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

thanks in advance!
Post edited by PencilxBoxes on

Replies to: Blue book math question

  • e2thepieyee2thepieye Registered User Posts: 22 New Member
    I could be wrong, but I believe you wrote down the problem incorrectly. I will go with (a^(1/2) x b^(1/3))^6 = 432, as is written in my copy. Just to clarify: a^1/2 is not necessarily equal to 1/a^2 (one situation in where it is equal is for 1. 1^(1/2) = 1/1^2). Getting back to the problem, the idea is to get rid of the 6. This is done by multiplying all exponents by 6. It follows from the rule that (ab)^n = a^n x b^n. Hence, a^(1/2 x 6) x b(1/3 x 6) = a^3 x b^2. That still equals 432. The question says they are positive integers, so that means we need to find a factorization of 432. We want one number to be a perfect cube and one to be a perfect square. We find that 27 x 16 works (to achieve this, find the prime factorization 2^4 x 3^3, call 3^3 the perfect cube, and 2^4 the perfect square). Call 27 = a^3, which means a = 3. Call 2^4 (which is 16) = b^2. b must then equal 4. Hence, the answer should be (B), or 12. Hope that helped.
  • PencilxBoxesPencilxBoxes Registered User Posts: 305 Junior Member
    ^Thanks! Yeah you're right, I actually read what was said in the book as what I had written above. Guess I need to take a more careful look next time!
  • xiggixiggi Registered User Posts: 25,441 Senior Member
    432 = 2^4 * 3^3
    a^3 * b^2 = 2^4 * 3^3 =
    3^3 * 4^2
    a=3, b=4, ab=12.
  • fogcityfogcity Registered User Posts: 3,228 Senior Member
    Possibly a quicker way to get the answer of "12", is to first rewrite the term:

    (a^1/2 x b^1/3) ^ 6 = a x (ab)^2

    So you want one positive integer times another positive integer squared to equal 432. The problem asks for that second positive integer -- the ab. You can go quickly through the list of choices (6, 12, 18, 24, and 36). ab can't be 24 or 36 -- the square is greater than 432. ab can't be 18 -- the square is 324, and so a would be 432/324 -- certainly not an integer. ab can't be 6, since that would mean that a is 12 (which is bigger than ab!). That leaves 12 squared (144), and observe that 144*3 is 432.
This discussion has been closed.