Sure! Let's evaluate the expression [tex]\(4! \cdot 3!\)[/tex] step-by-step.
### Step 1: Calculate [tex]\(4!\)[/tex]
The factorial of a number [tex]\(n\)[/tex] (written as [tex]\(n!\)[/tex]) is the product of all positive integers less than or equal to [tex]\(n\)[/tex]. So, for [tex]\(4!\)[/tex]:
[tex]\[
4! = 4 \times 3 \times 2 \times 1
\][/tex]
Calculating this:
[tex]\[
4 \times 3 = 12
\][/tex]
[tex]\[
12 \times 2 = 24
\][/tex]
[tex]\[
24 \times 1 = 24
\][/tex]
So, [tex]\(4! = 24\)[/tex].
### Step 2: Calculate [tex]\(3!\)[/tex]
Similarly, for [tex]\(3!\)[/tex]:
[tex]\[
3! = 3 \times 2 \times 1
\][/tex]
Calculating this:
[tex]\[
3 \times 2 = 6
\][/tex]
[tex]\[
6 \times 1 = 6
\][/tex]
So, [tex]\(3! = 6\)[/tex].
### Step 3: Multiply [tex]\(4!\)[/tex] and [tex]\(3!\)[/tex]
Now that we have [tex]\(4! = 24\)[/tex] and [tex]\(3! = 6\)[/tex], we need to multiply these two values together:
[tex]\[
4! \cdot 3! = 24 \cdot 6
\][/tex]
Calculating this:
[tex]\[
24 \times 6 = 144
\][/tex]
### Conclusion
Therefore, the result of the expression [tex]\(4! \cdot 3!\)[/tex] is 144. So, the correct answer is 144.
