We're given s = 8^(3/2) as the side length. If we square both sides then we have s^2 = [8^(3/2)]^2 = 8^3. Note how the '2's effectively cancel out. This is because we multiply the exponents (3/2) and 2 to get (3/2)*2 = (3/2)*(2/1) = (3*2)/(2*1) = 6/2 = 3.
So A = s^2 = 8^3 = 512 is the area of the square
