What is the digit at hundreds place of the number (25)^{10}?

Explanation

We can write 25^{10} as (625)^5 = (620 + 5)^5. Expanding using the binomial theorem, all terms except the last two end with at least three zeros. The last two terms are 5 \times 620 \times 5^4 + 5^5 = 1937500 + 3125 = 1940625. The hundreds digit is 6.

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