Sure, let's evaluate the expression [tex]\(4! \cdot 3!\)[/tex] step-by-step.
1. Calculate [tex]\(4!\)[/tex]:
- By definition, [tex]\(4!\)[/tex] (or 4 factorial) is the product of all positive integers up to 4.
- Therefore, [tex]\(4! = 4 \times 3 \times 2 \times 1\)[/tex].
- [tex]\(4! = 24\)[/tex].
2. Calculate [tex]\(3!\)[/tex]:
- Similarly, [tex]\(3!\)[/tex] (or 3 factorial) is the product of all positive integers up to 3.
- Therefore, [tex]\(3! = 3 \times 2 \times 1\)[/tex].
- [tex]\(3! = 6\)[/tex].
3. Multiply the results of [tex]\(4!\)[/tex] and [tex]\(3!\)[/tex]:
- We need to find [tex]\(4! \cdot 3!\)[/tex].
- From our calculations, we know [tex]\(4! = 24\)[/tex] and [tex]\(3! = 6\)[/tex].
- So, [tex]\(4! \cdot 3! = 24 \cdot 6\)[/tex].
4. Perform the multiplication:
- [tex]\(24 \cdot 6 = 144\)[/tex].
Therefore, the value of the expression [tex]\(4! \cdot 3! \)[/tex] is [tex]\(144\)[/tex].
So, the correct answer is [tex]\( \boxed{144} \)[/tex].
