  Let $\Omega$ be a bounded Reinhardt domain in $\mathbb{C}^n$ and
$\phi_1,\ldots,\phi_m$ be finite sums of bounded quasi-homogeneous functions.
We show that if the product of Toeplitz operators $T_{\phi_m}\cdots
T_{\phi_1}=0$ on the Bergman space on $\Omega$, then $\phi_j=0$ for some $j$.
