(N/A) The chemical formula of baking powder is sodium hydrogencarbonate $(NaHCO_3)$,while the chemical formula of washing soda is sodium carbonate decahydrate $(Na_2CO_3 \cdot 10H_2O)$.
When baking powder $(NaHCO_3)$ is heated,it undergoes thermal decomposition to release carbon dioxide $(CO_2)$ gas. This gas turns lime water milky.
$2NaHCO_3 \xrightarrow{\text{Heat}} Na_2CO_3 + H_2O + CO_2 \uparrow$
In contrast,washing soda $(Na_2CO_3 \cdot 10H_2O)$ loses its water of crystallization upon heating but does not release $CO_2$ gas. Therefore,it does not turn lime water milky.
$Na_2CO_3 \cdot 10H_2O \xrightarrow{\text{Heat}} Na_2CO_3 + 10H_2O$