 Solution

A holonomic constraint is $F(q,t)=0$. In the multiplier formulation its generalized constraint force is $Q_i=\lambda {\partial }_{i}F$. Along an allowed motion, its power is ${\sum }_i{Q}_i{\dot{q}}_i=\lambda (\dot{F}-{\partial }_{t}F)$, which vanishes when the constraint has no explicit time dependence.