Competition problem — Number theory

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Number theory Difficulty 2.4 Junior Find the answer

How many digits are in the product $4^5 \cdot 5^{10}$ ?

Pick one

Solution

$4^5 \cdot 5^{10} = 2^{10} \cdot 5^{10} = 10^{10}.$
That is one $1$ followed by ten $0$ 's, which is $\boxed{\textbf{(D)}\ 11}$ digits.

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Source: NuminaMath-1.5, licensed Apache-2.0. Statement and solution reproduced as published; topic and difficulty added by this site.