9. (5 points) A non-zero natural number $a$ satisfies the following two conditions:
(1) $0.2 a=m \times m$;
(2) $0.5 a=n \times n \times n$.
where $m, n$ are natural numbers, then the minimum value of $a$ is $\qquad$

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【Solution】Solution: $0.2 a=m^{2}, a=5 m^{2}, a$ contains the prime number 5, $0.5 a=n^{3}, a=2 n^{3}, a$ contains the prime number 2,

Therefore, $a$ contains prime factors 2 and 5. According to $a=5 m^{2}$, the number of 2s in $a$ is an even power. The number of 5s is an odd power. According to $a=2 n^{3}$, the number of 5s in $a$ is a multiple of 3. Removing one 2 from the even power makes it a cube number, the smallest being 4. Therefore, the smallest $a=2^{4} \times 5^{3}=2000$.

The answer is: 2000.