4. Let $A$ and $B$ be two sets, and $(A, B)$ is called a "pair". When $A \neq B$, $(A, B)$ and $(B, A)$ are considered different pairs. Then the number of different pairs satisfying the condition $A \cup B=\{1,2,3,4\}$ is $\qquad$
Prompt: Following Example 3, we know there are $3^{4}=81$ pairs.

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Prompt: Following Example 3, we know there are $3^{4}=81$ pairs.