Answer :
Final answer:
To simplify the expression 5!6!, we expand the factorials partially, cancel out common terms, and multiply the results. The simplified answer is 86400, which we confirmed is reasonable by checking the factorial calculations.
Explanation:
The question is asking to evaluate the expression 5!6! and simplify it. When simplifying factorial expressions, it's helpful to expand them partially to eliminate common terms and then simplify.
We can write 5! as 5×4×3×2×1 and 6! as 6×5×4×3×2×1, and since 5! is a subset of 6!, we can simplify 5!6! by canceling out the 5! terms:
• 5! = 5×4×3×2×1 = 120
• 6! = 6×5×4×3×2×1 = 6×120 = 720
• 5!6! = 120×720 = 86400
The simplified answer is 86400.
To check if the answer is reasonable, we can verify that 5! is indeed 120 and 6! is 720. Multiplying them gives us 86400, which matches our simplified result.
