  We give a short argument why the tensor product valuation on $K \otimes_k L$
is multiplicative when $k$ is an algebraically closed valued field and $K$ and
$L$ are valued extensions (all valuations being in $\bR$). When the valuation
on $k$ is non trivial we use the fact that $ACVF$, the theory of algebraically
closed (non trivially) valued fields, has quantifier elimination.
