Answer
Please see the work below.
Work Step by Step
We know that
$K_c=\frac{[product]^{coefficient }}{[reactant]^{coefficient }}$
$\implies K_c=\frac{[SO_3]^2}{[SO_2]^2[O_2]}$
We plug in the known values to obtain:
$K_c=\frac{(0.01480)^2}{0.005200(0.00260)}=3.11\times 10^3$