Why do we multiply (and not take the sum) the concentration of products and reactants when more than one entity is present in either side and rise the power to the coefficient term?
Suppose either
$$\ce{aA + bB <=> cC +dD}$$
described by
$$K_{\mathrm{eq}} = \frac{[\ce{C}]^c \cdot [\ce{D}]^d} {[\ce{A}]^a \cdot [\ce{B}]^b}$$
where we multiply the concentrations and rise the power to the coefficient. Or the dissociation of
$$\ce{A_aB_b <=> aA+ + bB-}$$
described by $$K_{\mathrm{sp}} = [\ce{A}]^a \cdot [\ce{B}]^b$$
again based on a product, and not the sum.
This seeks a clarification of math based on chemistry. How to explain it to an 8th grader?