3 [Divisibility of numbers. General properties]

It is known that $x=2 a^{5}=5 b^{2}>0$, where numbers $a$ and $b$ are integers. What is the smallest possible value of $x$?
The number $x$ is divisible by 2 and 5. $x=2 a^{5}$, so $a$ is divisible by 5. Since $x=5 b^{2}$, $x$ is divisible by $2^{2}$, which means $a$ is also divisible by 2. Assuming $a=2 \cdot 5=10$, we get $x=200000$ and $b=200$.

## Answer

200000.