Distributivity of Quotients of Countable Products of Boolean Algebras

We compute the distributivity numbers of algebras of the type $\mathbb{B}^{\omega}/ \mathrm{Fin}$ where $\mathbb{B}$ is the trivial algebra $\left\{0,1\right\}$, the countable atomless Boolean algebra, $\mathcal{P}\left(\omega\right)$, $\mathcal{P}\left(\omega\right)/\mathrm{fin}$ and $(\mathcal{P}(\omega)/\mathrm{fin})^{\omega}$.}