Exponent

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$x$ is an integer such that $x = n^k$

What is the last three digits of the smallest integer $k$ so that $x$ is a perfect square, perfect cube, perfect fourth power, perfect fifth power, ... , perfect tenth power?

The answer is 520.

1 solution

Daniel Lim
Jan 20, 2014

To ensure that $x$ is a perfect square, cube, and so on, $k$ must be divisible by $2, 3, 4, ..., 9, 10$

To get the smallest integer $k$ , we need to find the LCM of $2, 3, 4, ..., 10$ that is $2520$

So the answer is $\boxed{520}$

Exponent

The answer is 520.

1 solution

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