7. Let sets $A, B, C$ satisfy
$$
A \cup B \cup C=\{1,2, \cdots, 9\} \text {. }
$$

Then the number of ordered triples $(A, B, C)$ is $\qquad$ .
Ni,7.7 ${ }^{9}$.
Place the numbers $1 \sim 9$ into three sets $A$, $B$, and $C$. First, consider the number 1 separately.
When the number 1 appears once, twice, or three times, the number of placement methods are $\mathrm{C}_{3}^{1}$, $\mathrm{C}_{3}^{2}$, and $\mathrm{C}_{3}^{3}$, respectively.
Therefore, the total number of ways to place the number 1 is $\mathrm{C}_{3}^{1}+\mathrm{C}_{3}^{2}+\mathrm{C}_{3}^{3}=7$. Similarly, the number of placement methods for the other eight numbers is also 7. Thus, the total number of ordered triples $(A, B, C)$ is $7^{9}$.