  Let $\{P_i\}_{1 \leq i \leq r}$ and $\{Q_i\}_{1 \leq i \leq r}$ be two
collections of Brauer Severi surfaces (resp. conics) over a field $k$. We show
that the subgroup generated by the $P_i's$ in $Br(k)$ is the same as the
subgroup generated by the $Q_i's$ \iff $\Pi P_i $ is birational to $\Pi Q_i$.
Moreover in this case $\Pi P_i$ and $\Pi Q_i$ represent the same class in
$M(k)$, the Grothendieck ring of $k$-varieties. The converse holds if
$char(k)=0$. Some of the above implications also hold over a general noetherian
base scheme.
