AMC8 2011 8, Problem 15

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

Solution: \[4^5 \cdot 5^{10} = 2^{10} \cdot 5^{10} = 10^{10}.\] That is one $1$ followed by ten $0$'s, which is $\fbox{11}$ digits.

Answer: 11