  In this note, we are interested in local-global principles for multinorm
equations of the form $\prod_{i=1}^n N_{L_i /k}(z_i) = a$ where $k$ is a global
field, $L_i/k$ are finite separable field extensions and $a \in k^*$.
  In particular, we prove a result relating weak approximation for this
equation to weak approximation for some classical norm equation $N_{F/k}(w) =
a$ where $F := \bigcap_{i=1}^n L_i$. It provides a proof of a "weak
approximation" analogue of a recent conjecture by Pollio and Rapinchuk about
multinorm principle. We also provide a counterexample to the original
conjecture concerning Hasse principle.
