another one :) ?

Question

if a and b are positive integers and (a^1/2 b^1/3)^6 = 432, what is the value of ab?
the answer is 12 but I don't know how to sove it, could you please explain it to me step by step?
thanks in advance.

Answer 1

(a^1/2b^1/3)^6 = 432
a^3 b^2 = 4 * 4 * 3 * 3 * 3 = 4^2 * 3^3
Since, a and 3 have the same power, they are equal. And because b and 4 have the same power, they are equal.
a = 3, b = 4
ab = 12

Answer 2

(a^1/2b^1/3)^6=432
=> a^(1/2X6)b^(1/3X6)=432
=>a^3b^2=432
=>a*a*a*b*b=3*3*3*4*4
therefore a=3 and b=4
ab=3*4=12