In the prime factorization of $24!$, what is the exponent of $3$? (Reminder: The number $n!$ is the product of the integers from 1 to $n$. For example, $\(5!=5\cdot 4\cdot3\cdot2\cdot 1= 120$.\))

24/3=8.

At first glance, the answer might seem like 8, but this is a wrong assumption.

This is because the numbers 9 and 18 hold two nines!

so we need to add two to 8 to have 10 as our answer.