2016 AMC 10B Problem 2

For any nonzero $a,b,$ we have $$\dfrac{a\heartsuit b}{b\heartsuit a} = \dfrac{a^3b^2}{b^3 a^2} = \dfrac ab .$$ Using $a=2,b=4,$ we get that $\frac{ 2}{4} = \frac 12.$ Thus, the correct answer is B .