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

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Question 93751: If a and b are positive integers and (a^1/2 b^1/3)^6 = 432, what is the value of ab?
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
If a and b are positive integers and (a^1/2 b^1/3)^6 = 432, what is the value of ab?
:
%28a%5E%281%2F2%29%2Ab%5E%281%2F3%29%29%5E6 = 432
:
%28a%5E%286%2F2%29%2Ab%5E%286%2F3%29%29 = 432
:
a%5E3+%2A+b%5E2 = 432
:
Checking for some suitable factors of 432, we come up with
a%5E3+%2A+b%5E2 = 27 * 16
:
if a = 3; 3^3 = 27
and
if b = 4; 4^2 = 16
:
a*b = 12
:
There may be a more orthodox way to do this, but I can't seem to come up with it today.