Algebra Examples

$a_{4} = \frac{4^{3}}{4!}$

Raise $4$ to the power of $3$ .

$a_{4} = \frac{64}{4!}$

Simplify the denominator.

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

$a_{4} = \frac{64}{4 \cdot 3 \cdot 2 \cdot 1}$

Simplify.

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Multiply $4$ by $3$ .

$a_{4} = \frac{64}{12 \cdot 2 \cdot 1}$

Multiply $12$ by $2$ .

$a_{4} = \frac{64}{24 \cdot 1}$

Multiply $24$ by $1$ .

$a_{4} = \frac{64}{24}$

$a_{4} = \frac{64}{24}$

$a_{4} = \frac{64}{24}$

Cancel the common factor of $64$ and $24$ .

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Factor $8$ out of $64$ .

$a_{4} = \frac{8 (8)}{24}$

Cancel the common factors.

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Factor $8$ out of $24$ .

$a_{4} = \frac{8 \cdot 8}{8 \cdot 3}$

Cancel the common factor.

$a_{4} = \frac{8 \cdot 8}{8 \cdot 3}$

Rewrite the expression.

$a_{4} = \frac{8}{3}$

$a_{4} = \frac{8}{3}$

$a_{4} = \frac{8}{3}$

The result can be shown in multiple forms.

Exact Form:

$a_{4} = \frac{8}{3}$

Decimal Form:

$a_{4} = 2.\overline{6}$

Mixed Number Form:

$a_{4} = 2 \frac{2}{3}$

$[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]$