Basic Math Examples

$\frac{12!}{4! 4! 4! 4!}$

Step 1

Multiply $4!$ by $4!$ .

$\frac{12!}{{4!}^{2} 4! 4!}$

Step 2

Multiply ${4!}^{2}$ by $4!$ by adding the exponents.

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Step 2.1

Multiply ${4!}^{2}$ by $4!$ .

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Step 2.1.1

Raise $4!$ to the power of $1$ .

$\frac{12!}{{4!}^{2} {4!}^{1} 4!}$

Step 2.1.2

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\frac{12!}{{4!}^{2 + 1} 4!}$

Step 2.2

Add $2$ and $1$ .

$\frac{12!}{{4!}^{3} 4!}$

Step 3

Multiply ${4!}^{3}$ by $4!$ by adding the exponents.

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Step 3.1

Multiply ${4!}^{3}$ by $4!$ .

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Step 3.1.1

Raise $4!$ to the power of $1$ .

$\frac{12!}{{4!}^{3} {4!}^{1}}$

Step 3.1.2

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\frac{12!}{{4!}^{3 + 1}}$

Step 3.2

Add $3$ and $1$ .

$\frac{12!}{{4!}^{4}}$

Step 4

Simplify the numerator.

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Step 4.1

Expand $12!$ to $12 \cdot 11 \cdot 10 \cdot 9 \cdot 8 \cdot 7 \cdot 6 \cdot 5 \cdot 4 \cdot 3 \cdot 2 \cdot 1$ .

$\frac{12 \cdot 11 \cdot 10 \cdot 9 \cdot 8 \cdot 7 \cdot 6 \cdot 5 \cdot 4 \cdot 3 \cdot 2 \cdot 1}{{4!}^{4}}$

Step 4.2

Multiply $12 \cdot 11 \cdot 10 \cdot 9 \cdot 8 \cdot 7 \cdot 6 \cdot 5 \cdot 4 \cdot 3 \cdot 2 \cdot 1$ .

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Step 4.2.1

Multiply $12$ by $11$ .

$\frac{132 \cdot 10 \cdot 9 \cdot 8 \cdot 7 \cdot 6 \cdot 5 \cdot 4 \cdot 3 \cdot 2 \cdot 1}{{4!}^{4}}$

Step 4.2.2

Multiply $132$ by $10$ .

$\frac{1320 \cdot 9 \cdot 8 \cdot 7 \cdot 6 \cdot 5 \cdot 4 \cdot 3 \cdot 2 \cdot 1}{{4!}^{4}}$

Step 4.2.3

Multiply $1320$ by $9$ .

$\frac{11880 \cdot 8 \cdot 7 \cdot 6 \cdot 5 \cdot 4 \cdot 3 \cdot 2 \cdot 1}{{4!}^{4}}$

Step 4.2.4

Multiply $11880$ by $8$ .

$\frac{95040 \cdot 7 \cdot 6 \cdot 5 \cdot 4 \cdot 3 \cdot 2 \cdot 1}{{4!}^{4}}$

Step 4.2.5

Multiply $95040$ by $7$ .

$\frac{665280 \cdot 6 \cdot 5 \cdot 4 \cdot 3 \cdot 2 \cdot 1}{{4!}^{4}}$

Step 4.2.6

Multiply $665280$ by $6$ .

$\frac{3991680 \cdot 5 \cdot 4 \cdot 3 \cdot 2 \cdot 1}{{4!}^{4}}$

Step 4.2.7

Multiply $3991680$ by $5$ .

$\frac{19958400 \cdot 4 \cdot 3 \cdot 2 \cdot 1}{{4!}^{4}}$

Step 4.2.8

Multiply $19958400$ by $4$ .

$\frac{79833600 \cdot 3 \cdot 2 \cdot 1}{{4!}^{4}}$

Step 4.2.9

Multiply $79833600$ by $3$ .

$\frac{239500800 \cdot 2 \cdot 1}{{4!}^{4}}$

Step 4.2.10

Multiply $239500800$ by $2$ .

$\frac{479001600 \cdot 1}{{4!}^{4}}$

Step 4.2.11

Multiply $479001600$ by $1$ .

$\frac{479001600}{{4!}^{4}}$

Step 5

Simplify the denominator.

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Step 5.1

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

$\frac{479001600}{{(4 \cdot 3 \cdot 2 \cdot 1)}^{4}}$

Step 5.2

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

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Step 5.2.1

Multiply $4$ by $3$ .

$\frac{479001600}{{(12 \cdot 2 \cdot 1)}^{4}}$

Step 5.2.2

Multiply $12$ by $2$ .

$\frac{479001600}{{(24 \cdot 1)}^{4}}$

Step 5.2.3

Multiply $24$ by $1$ .

$\frac{479001600}{24^{4}}$

Step 5.3

Raise $24$ to the power of $4$ .

$\frac{479001600}{331776}$

Step 6

Cancel the common factor of $479001600$ and $331776$ .

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Step 6.1

Factor $82944$ out of $479001600$ .

$\frac{82944 (5775)}{331776}$

Step 6.2

Cancel the common factors.

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Step 6.2.1

Factor $82944$ out of $331776$ .

$\frac{82944 \cdot 5775}{82944 \cdot 4}$

Step 6.2.2

Cancel the common factor.

$\frac{82944 \cdot 5775}{82944 \cdot 4}$

Step 6.2.3

Rewrite the expression.

$\frac{5775}{4}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$\frac{5775}{4}$

Decimal Form:

$1443.75$

Mixed Number Form:

$1443 \frac{3}{4}$