Evaluate the factorial expression. \[ \frac{23 !}{15 !} \] \[ \frac{23 !}{15 !}= \]

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 are asked to evaluate the ratio of \(23!\) to \(15!\). We can simplify this by cancelling out the common terms in the numerator and the denominator.

Step 3 ：The factorial of 23 (\(23!\)) is the product of all positive integers from 23 down to 1. The factorial of 15 (\(15!\)) is the product of all positive integers from 15 down to 1.

Step 4 ：We can write \(23!\) as \((23*22*21*20*19*18*17*16*15!)\), and \(15!\) as \((15*14*13*12*11*10*9*8*7*6*5*4*3*2*1)\).

Step 5 ：When we divide \(23!\) by \(15!\), all the terms from 15 down to 1 in the numerator and the denominator will cancel out.

Step 6 ：So, the expression simplifies to the product of the integers from 23 down to 16, which is 19769460480.

Step 7 ：Final Answer: \(\boxed{19769460480}\)