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PencilxBoxes
Registered User Posts: **305** Junior Member

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

b)12

c)18

d)24

e)36

thanks in advance!

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

a) 6

b)12

c)18

d)24

e)36

thanks in advance!

Post edited by PencilxBoxes on

This discussion has been closed.

## Replies to: Blue book math question

22New Member305Junior Member25,441Senior Membera^3 * b^2 = 2^4 * 3^3 =

3^3 * 4^2

a=3, b=4, ab=12.

3,228Senior Member(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.