1. If the set of real numbers
$$
A=\{2 x, 3 y\} \text { and } B=\{6, x y\}
$$

have exactly one common element, then the product of all elements in $A \cup B$ is $\qquad$ .
-1.0 .
Let the unique common element of sets $A$ and $B$ be denoted as $a$. If $a \neq 0$, then the other elements of sets $A$ and $B$ are both $\frac{6 x y}{a}$, which is a contradiction.
Therefore, the product of all elements in $A \cup B$ is 0.