Solving the expressions below, which result ends with the largest number of zeros?

a) $2^{5} \cdot 3^{4} \cdot 5^{6}$.

b) $2^{4} \cdot 3^{4} \cdot 5^{5}$.

c) $4^{3} \cdot 5^{6} \cdot 6^{5}$.

d) $4^{2} \cdot 5^{4} \cdot 6^{3}$.
Solution

Since $2^{5} \cdot 3^{4} \cdot 5^{6}=10^{5} \cdot 3^{4} \cdot 5$ ends with 5 zeros, $2^{4} \cdot 3^{4} \cdot 5^{5}=10^{4} \cdot 3^{4} \cdot 5$ ends with 4 zeros, $4^{3} \cdot 5^{6} \cdot 6^{5}=10^{6} \cdot 6^{5}$ ends with 6 zeros, and $4^{2} \cdot 5^{4} \cdot 6^{3}=10^{4} \cdot 6^{3}$ ends with 4 zeros, the correct option is letter $C$.