A student models a halide-exchange step that can occur when silver halide solids contact an aqueous sample. At \(25^\circ\text{C}\), the equilibrium constants for the dissolution reactions are given below.

Equilibrium	Equilibrium constant
\(\text{AgCl(s)} \rightleftharpoons \text{Ag}^+\text{(aq)} + \text{Cl}^-\text{(aq)}\)	\(K_1=2.0\times10^{-10}\)
\(\text{AgBr(s)} \rightleftharpoons \text{Ag}^+\text{(aq)} + \text{Br}^-\text{(aq)}\)	\(K_2=5.0\times10^{-13}\)

The student combines the equilibria to represent the net reaction \(\text{AgCl(s)}+\text{Br}^-\text{(aq)}\rightleftharpoons\text{AgBr(s)}+\text{Cl}^-\text{(aq)}\). What is the value of \(K\) for this net reaction at \(25^\circ\text{C}\)?