(a +3)^2 + |3b - 1| = 0 ==> a + 3= 0,3b -1 = 0 ==> a = -3,b = 1/3 a^2010 * b^2011 = (ab)^2010 * b = (-1)^2010 * (1/3) = 1 * (1/3) = 1/3