How many digits are located to the right of the decimal point when $\frac{3^6}{6^4\cdot625}$ is expressed as a decimal?
I know that 625 is a power of 5, namely 5^4. So I can rewrite the denominator as 6^4\cdot5^4. I get $\frac{3^6}{(2\cdot3)^4\cdot5^4}$. I get $\frac{3^6}{2^4\cdot3^4\cdot5^4}$. I get $\frac{3^2}{2^4\cdot5^4}$. This is the same as $\frac{9}{(2\cdot5)^4}$. I get $\frac{9}{10^4}$. This is a decimal fraction with 4 digits after the decimal point. So the answer is 4. 