Evaluate. Express your answer in exact simplest form. \[ \frac{120 !}{117 !}= \]

Step 1 ：The factorial of a number n, denoted as n!, is the product of all positive integers less than or equal to n. For example, \(5! = 5*4*3*2*1 = 120\).

Step 2 ：In the given expression, we have \(120!\) divided by \(117!\). This can be simplified by cancelling out the common terms in the numerator and the denominator.

Step 3 ：The factorial of 120, \(120!\), is the product of all positive integers from 1 to 120. Similarly, the factorial of 117, \(117!\), is the product of all positive integers from 1 to 117.

Step 4 ：Therefore, when we divide \(120!\) by \(117!\), all the terms from 1 to 117 in the numerator and the denominator will cancel out, leaving us with the product of the integers from 118 to 120 in the numerator.

Step 5 ：So, the expression simplifies to \(120*119*118\).

Step 6 ：Calculating the product, we get \(1685040\).

Step 7 ：Final Answer: The exact simplest form of the given expression is \(\boxed{1685040}\).