Autoprotolysis constant of a weak acid HA is 4x 10^-8. Hence, [A^-] is

In autoprotolysis, a proton is transferred between two identical molecules:

$$\begin{gathered} \mathrm{HA}+\mathrm{HA}\rightleftharpoons {\mathrm{H}}_2{\mathrm{A}}^{-}+{\mathrm{A}}^{-} \\ \left[{\mathrm{H}}_2{\mathrm{A}}^{-}\right]=\left[{\mathrm{A}}^{-}\right] \\ \mathrm{K}=\left[{\mathrm{H}}_2{\mathrm{A}}^{-}\right]\left[{\mathrm{A}}^{-}\right]=4\times {10}^{-8} \\ {\left[{\mathrm{H}}_2{\mathrm{A}}^{-}\right]}^2={\left[{\mathrm{A}}^{-}\right]}^2=4\times {10}^{-8} \\ \left[{\mathrm{A}}^{-}\right]=2\times {10}^{-4}\mathrm{M} \end{gathered}$$