# Thread: Stuck on an SAT problem

1. ## Stuck on an SAT problem

Hello,
I go this from an SAT practice book. Unfortunatly it does not show the solution. This is the problem:

2. $432=2^4*3^3$
So if $432=a^3*b^2$ and a and b are positive integer then a can only contain prime factors 2 and 3. And the power of each prime factor cannot be greater then 1. The power of 2 is equal to 0 because if it is equal to 1 then $b^2$ must contain $2^1$ which is impossible. The power of 3 cannot be equal to 0 because in such case $b^2$ must contain $3^3$ which is impossible. So $a=3$ then $b=4$ and $ab=12$