Evaluate the expression.
$\frac{9!}{7!}$

• A. 2!
• B. 63
• C. 72
• D. 98

Answer: (C)

Verified step by step guidance

1. Understand that a factorial, denoted by \(n!\), is the product of all positive integers from 1 up to \(n\). For example, \$5! = 5 \times 4 \times 3 \times 2 \times 1$.
2. Identify the factorial expressions given in the problem that need to be simplified or factored.
3. Rewrite each factorial expression by expanding it into its product form to see common factors clearly. For example, \$7! = 7 \times 6 \times 5 \times 4 \times 3 \times 2 \times 1$.
4. Look for common factorial terms or factors that can be factored out. For example, if you have \$7! + 6!\(, express both in terms of \)6!\( to factor it out: \)7! = 7 \times 6!$.
5. Use the factored form to simplify the expression further by factoring out the common factorial and then simplifying the remaining terms inside the parentheses.