Mathcounts Countdown Question?

About three Months ago, I saw someone correctly answer this question in a mathcounts countdown round in the chapter competition. Here's the question.

If the product (1^1)(2^2)(3^3)(4^4)(5^5) ... (10^10)
is written as an integer, how many zeros are to the right of the right-most non-zero
digit?

The answer was 15 zeroes, but I don't know why. Can someone explain why the answer is 15.
 
Back
Top