Derive the equation for the solubility and solubility product of a sparingly soluble salt $M_{x}X_{y}$.

(N/A) Consider a sparingly soluble salt $M_{x}X_{y}$ with solubility $S \ mol \ L^{-1}$.
The dissociation equilibrium is:
$M_{x}X_{y(s)} \rightleftharpoons x M_{(aq)}^{p+} + y X_{(aq)}^{q-}$
At equilibrium,the concentrations are $[M^{p+}] = xS$ and $[X^{q-}] = yS$.
The solubility product constant $K_{sp}$ is defined as:
$K_{sp} = [M^{p+}]^{x} [X^{q-}]^{y}$
Substituting the values of concentrations:
$K_{sp} = (xS)^{x} (yS)^{y}$
$K_{sp} = x^{x} y^{y} S^{(x+y)}$
Rearranging for solubility $S$:
$S^{(x+y)} = \frac{K_{sp}}{x^{x} y^{y}}$
$S = \left( \frac{K_{sp}}{x^{x} y^{y}} \right)^{\frac{1}{x+y}}$