You can put this solution on YOUR website! When you raise something to the third power, you multiply by itself 3 times. So (3a^3b^2)^3 = (3a^3b^2)*(3a^3b^2)*(3a^3b^2). But (3a^3b^2)^2 = (3a^3b^2)*(3a^3b^2). So that's two of the three from (3a^3b^2)*(3a^3b^2)*(3a^3b^2). So:
(3a^3b^2)^3= (3a^3b^2)^2*(3a^3b^2)