Question 93751
If a and b are positive integers and (a^1/2 b^1/3)^6 = 432, what is the value of ab?
:
{{{(a^(1/2)*b^(1/3))^6}}} = 432
:
{{{(a^(6/2)*b^(6/3))}}} = 432
:
{{{a^3 * b^2}}} = 432
:
Checking for some suitable factors of 432, we come up with
{{{a^3 * b^2}}} = 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.