This problem involves exponents and division, so I want to simplify it as much as possible. One way to do that is to write both numbers in terms of the same base, since that makes it easier to compare their powers. I notice that both 36 and 6 are multiples of 6, so I can write 36 as $6^2$. Then, $36^{10} = (6^2)^{10} = 6^{20}$, by the power of a power rule. Now I have $6^{20} \div 6^{19}$, which is much simpler. To divide two numbers with the same base, I can subtract their exponents. So, $6^{20} \div 6^{19} = 6^{20-19} = 6^1 = 6$. 
Compute $36^{10} \div 6^{19}$.