Algebra Examples

$\frac{6!}{0! (6 - 0)!}$

Step 1

Simplify the numerator.

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Step 1.1

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

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

Step 1.2

Multiply $6 \cdot 5 \cdot 4 \cdot 3 \cdot 2 \cdot 1$ .

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Step 1.2.1

Multiply $6$ by $5$ .

$\frac{30 \cdot 4 \cdot 3 \cdot 2 \cdot 1}{0! (6 - 0)!}$

Step 1.2.2

Multiply $30$ by $4$ .

$\frac{120 \cdot 3 \cdot 2 \cdot 1}{0! (6 - 0)!}$

Step 1.2.3

Multiply $120$ by $3$ .

$\frac{360 \cdot 2 \cdot 1}{0! (6 - 0)!}$

Step 1.2.4

Multiply $360$ by $2$ .

$\frac{720 \cdot 1}{0! (6 - 0)!}$

Step 1.2.5

Multiply $720$ by $1$ .

$\frac{720}{0! (6 - 0)!}$

Step 2

Simplify the denominator.

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Step 2.1

Expand $0!$ to $1$ .

$\frac{720}{1 (6 - 0)!}$

Step 2.2

Subtract $0$ from $6$ .

$\frac{720}{1 (6)!}$

Step 2.3

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

$\frac{720}{1 (6 \cdot 5 \cdot 4 \cdot 3 \cdot 2 \cdot 1)}$

Step 2.4

Multiply $6 \cdot 5 \cdot 4 \cdot 3 \cdot 2 \cdot 1$ .

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Step 2.4.1

Multiply $6$ by $5$ .

$\frac{720}{1 (30 \cdot 4 \cdot 3 \cdot 2 \cdot 1)}$

Step 2.4.2

Multiply $30$ by $4$ .

$\frac{720}{1 (120 \cdot 3 \cdot 2 \cdot 1)}$

Step 2.4.3

Multiply $120$ by $3$ .

$\frac{720}{1 (360 \cdot 2 \cdot 1)}$

Step 2.4.4

Multiply $360$ by $2$ .

$\frac{720}{1 (720 \cdot 1)}$

Step 2.4.5

Multiply $720$ by $1$ .

$\frac{720}{1 \cdot 720}$

Step 2.5

Multiply $720$ by $1$ .

$\frac{720}{720}$

Step 3

Divide $720$ by $720$ .

$1$