Why are the reactants in the solubility product constant multiplied by their coefficients and raised to the power of their coefficients?
The reason why in the equilibrium constant expression, the concentration is to the power of coefficient is because the above equation can be written like this:
$$\ce{MgF_2(s) -&gt; Mg^{2+} (aq) + F^- + F^- (aq)}$$
Hence when you plug this into the equilibrium constant expression, you get this:
$$K_{sp}=[\ce{Mg^{2+}}][\ce{F-}][\ce{F-}]$$ which becomes the equivalent to:$$K_{sp}=[\ce{Mg^{2+}}][\ce{F-}]^{2}$$ So really the equilibrium constant is proportional to the square of the concentration of fluoride. So that is the reason for the square. However, the concentration of fluoride is twice as much as the concentration of Mg, hence that is the reason for the multiplying the concentration of fluoride by 2. So that is why fluoride is denoted as $(2X)^2$.