The following equilibrium constants are given:

Target reaction: $2{\text{NH}}_3+\frac{5}{2}{\text{O}}_2\rightleftharpoons 2\text{NO}+3{\text{H}}_2\text{O}$ Steps to reach target:Reverse reaction (1): $2{\text{NH}}_3\rightleftharpoons {\text{N}}_2+3{\text{H}}_2$, $K^{\prime }=\frac{1}{K_1}$ Use reaction (2): ${\text{N}}_2+{\text{O}}_2\rightleftharpoons 2\text{NO}$, $K^{\prime \prime }=K_2$ Multiply reaction (3) by 3: $3{\text{H}}_2+\frac{3}{2}{\text{O}}_2\rightleftharpoons 3{\text{H}}_2\text{O}$, $K^{\prime \prime \prime }=K_3^3$ Summing these gives the target reaction. The net $K$ is the product of individual constants:$K_{net}=\frac{1}{K_1}\times K_2\times K_3^3=\frac{K_2{K}_3^3}{K_1}$