Questions: Find the exact value of the following expressions. a) (3 · 3) ! b) 3 ! 3 ! c) Is (3 · 3) ! equal to 3 ! 3 ! ? Yes No

Solution Steps

a) To find the exact value of \((3 \cdot 3)!\), first calculate the product \(3 \cdot 3\), then compute the factorial of the result.

b) To find the value of \(3! \cdot 3!\), compute the factorial of 3, and then multiply the result by itself.

c) To determine if \((3 \cdot 3)!\) is equal to \(3! \cdot 3!\), compare the results from parts a and b.

First, we compute the product: \[ 3 \cdot 3 = 9 \] Next, we find the factorial of 9: \[ 9! = 362880 \]

We calculate the factorial of 3: \[ 3! = 6 \] Then, we compute the product of \(3!\) with itself: \[ 3! \cdot 3! = 6 \cdot 6 = 36 \]

Now, we compare the two results: \[ (3 \cdot 3)! = 362880 \quad \text{and} \quad 3! \cdot 3! = 36 \] Since \(362880 \neq 36\), we conclude that: \[ (3 \cdot 3)! \text{ is not equal to } 3! \cdot 3! \]

Final Answer