Every factor of 36 is written on its own card, and then all the cards are multiplied together. The result is:

Since $36=2^2\times 3^2$, there are $(2+1)(2+1)=9$ cards. Pair them from the outside inwards — $1\times 36,2\times 18,3\times 12,4\times 9$ — so each pair multiplies to 36, leaving the middle card 6 unpaired. That is four 36s and one 6: $36^4\times 6=6^8\times 6=6^9$. In general the answer is n raised to half the number of factors, so using the full count instead of half gives the wrong answer $36^9$.