What is the sum of the digits of the decimal representation of $2^{2005} \times 5^{2007} \times 3$?
I want to find the sum of the digits of a very large number. One way to approach this problem is to try to write the number in a simpler form, using scientific notation or some other exponent rules. I notice that $2^{2005} \times 5^{2007} \times 3$ has a factor of $10^{2005}$, since $10 = 2 \times 5$. So I can write $2^{2005} \times 5^{2007} \times 3 = 10^{2005} \times 5^2 \times 3$. This means that the number has $2005$ zeros at the end, and the first few digits are given by $5^2 \times 3 = 75$. So the decimal representation of the number is $75$ followed by $2005$ zeros. To find the sum of the digits, I just need to add $7$ and $5$, since the rest of the digits are zeros. The sum of the digits is $7 + 5 = 12$. 