Evaluate (9!)/(0!(9-0)!)

$\frac{9!}{0! (9 - 0)!}$

Step 1

Simplify the numerator.

Expand $9!$ to $9 \cdot 8 \cdot 7 \cdot 6 \cdot 5 \cdot 4 \cdot 3 \cdot 2 \cdot 1$ .

$\frac{9 \cdot 8 \cdot 7 \cdot 6 \cdot 5 \cdot 4 \cdot 3 \cdot 2 \cdot 1}{0! (9 - 0)!}$

Multiply $9 \cdot 8 \cdot 7 \cdot 6 \cdot 5 \cdot 4 \cdot 3 \cdot 2 \cdot 1$ .

Multiply $9$ by $8$ .

$\frac{72 \cdot 7 \cdot 6 \cdot 5 \cdot 4 \cdot 3 \cdot 2 \cdot 1}{0! (9 - 0)!}$

Multiply $72$ by $7$ .

$\frac{504 \cdot 6 \cdot 5 \cdot 4 \cdot 3 \cdot 2 \cdot 1}{0! (9 - 0)!}$

Multiply $504$ by $6$ .

$\frac{3024 \cdot 5 \cdot 4 \cdot 3 \cdot 2 \cdot 1}{0! (9 - 0)!}$

Multiply $3024$ by $5$ .

$\frac{15120 \cdot 4 \cdot 3 \cdot 2 \cdot 1}{0! (9 - 0)!}$

Multiply $15120$ by $4$ .

$\frac{60480 \cdot 3 \cdot 2 \cdot 1}{0! (9 - 0)!}$

Multiply $60480$ by $3$ .

$\frac{181440 \cdot 2 \cdot 1}{0! (9 - 0)!}$

Multiply $181440$ by $2$ .

$\frac{362880 \cdot 1}{0! (9 - 0)!}$

Multiply $362880$ by $1$ .

$\frac{362880}{0! (9 - 0)!}$

Step 2

Simplify the denominator.

Expand $0!$ to $1$ .

$\frac{362880}{1 (9 - 0)!}$

Subtract $0$ from $9$ .

$\frac{362880}{1 (9)!}$

Expand $(9)!$ to $9 \cdot 8 \cdot 7 \cdot 6 \cdot 5 \cdot 4 \cdot 3 \cdot 2 \cdot 1$ .

$\frac{362880}{1 (9 \cdot 8 \cdot 7 \cdot 6 \cdot 5 \cdot 4 \cdot 3 \cdot 2 \cdot 1)}$

Multiply $9 \cdot 8 \cdot 7 \cdot 6 \cdot 5 \cdot 4 \cdot 3 \cdot 2 \cdot 1$ .

Multiply $9$ by $8$ .

$\frac{362880}{1 (72 \cdot 7 \cdot 6 \cdot 5 \cdot 4 \cdot 3 \cdot 2 \cdot 1)}$

Multiply $72$ by $7$ .

$\frac{362880}{1 (504 \cdot 6 \cdot 5 \cdot 4 \cdot 3 \cdot 2 \cdot 1)}$

Multiply $504$ by $6$ .

$\frac{362880}{1 (3024 \cdot 5 \cdot 4 \cdot 3 \cdot 2 \cdot 1)}$

Multiply $3024$ by $5$ .

$\frac{362880}{1 (15120 \cdot 4 \cdot 3 \cdot 2 \cdot 1)}$

Multiply $15120$ by $4$ .

$\frac{362880}{1 (60480 \cdot 3 \cdot 2 \cdot 1)}$

Multiply $60480$ by $3$ .

$\frac{362880}{1 (181440 \cdot 2 \cdot 1)}$

Multiply $181440$ by $2$ .

$\frac{362880}{1 (362880 \cdot 1)}$

Multiply $362880$ by $1$ .

$\frac{362880}{1 \cdot 362880}$

Multiply $362880$ by $1$ .

$\frac{362880}{362880}$

Step 3

Divide $362880$ by $362880$ .

$1$

Evaluate (9!)/(0!(9-0)!)

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