Algebra Examples

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

Step 1

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

$a_{3} = \frac{27}{3!}$

Step 2

Simplify the denominator.

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

$a_{3} = \frac{27}{3 \cdot 2 \cdot 1}$

Multiply $3 \cdot 2 \cdot 1$ .

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Multiply $3$ by $2$ .

$a_{3} = \frac{27}{6 \cdot 1}$

Multiply $6$ by $1$ .

$a_{3} = \frac{27}{6}$

$a_{3} = \frac{27}{6}$

$a_{3} = \frac{27}{6}$

Step 3

Cancel the common factor of $27$ and $6$ .

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Factor $3$ out of $27$ .

$a_{3} = \frac{3 (9)}{6}$

Cancel the common factors.

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Factor $3$ out of $6$ .

$a_{3} = \frac{3 \cdot 9}{3 \cdot 2}$

Cancel the common factor.

$a_{3} = \frac{3 \cdot 9}{3 \cdot 2}$

Rewrite the expression.

$a_{3} = \frac{9}{2}$

$a_{3} = \frac{9}{2}$

$a_{3} = \frac{9}{2}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$a_{3} = \frac{9}{2}$

Decimal Form:

$a_{3} = 4.5$

Mixed Number Form:

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

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