How many digits are in the product 4^5 · 5^10 ?

AMC 8 2011 Problem 15

AMC8 2011 年第 15 题

整除与因数★★★☆☆

How many digits are in the product

4^5 \cdot 5^{10}

的乘积结果有多少位数字？

正确答案 · Correct Answer

Solution 1

4^5 \cdot 5^{10} = 2^{10} \cdot 5^{10} = 10^{10}.

That is one 1 followed by ten 0 's, which is 11 digits.

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