smc

If $a=0$ or $c=0$, the expression evaluates to $-d<0$. If $b=0$, the expression evaluates to $c-d\le 2$. Case $d=0$ remains. In that case, we want to maximize $c\cdot a^b$ where $\{a,b,c\}=\{1,2,3\}$. Trying out the six possibilities we get that the greatest is $(a,b,c)=(3,2,1)$, where $c\cdot a^b=1\cdot 3^2=\boxed{9}$.