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# Digits

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36
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What is the sum of the final three digits of the integer representation of 5^{100}*2^{100}?

May 14, 2022

#1
+1810
+1

Note that $$5 \times 2 = 10$$.

We have 100 pairs of these, so the answer is $$10 ^ {100}$$

Becuase the base is 10, the answer is simply a 1, followed by the amount of trailing 0's in all the terms being multipoled.

This means that the answer is 1, followed by 100 zeros.

Can you find the sum of the last 3 digits from here?

May 14, 2022