At 298 K , the equilibrium constant is $2 \times 10^{15}$ for the reaction: $ \mathrm{Cu}(\mathrm{~s})+2 \mathrm{Ag}^{+}(\mathrm{aq}) \rightleftharpoons \mathrm{Cu}^{2+}(\mathrm{aq})+2 \mathrm{Ag}(\mathrm{~s}) $ The equilibrium constant for the reaction
$ \frac{1}{2} \mathrm{Cu}^{2+}(\mathrm{aq})+\mathrm{Ag}(\mathrm{~s}) \rightleftharpoons \frac{1}{2} \mathrm{Cu}(\mathrm{~s})+\mathrm{Ag}^{+}(\mathrm{aq})
$ is $x \times 10^{-8}$. The value of $x$ is $\_\_\_\_$ .