Basic Math Examples

$\frac{1}{4} \cdot (\frac{1}{36}) + {(- \frac{1}{12})}^{2}$

Step 1

Simplify each term.

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Step 1.1

Multiply $\frac{1}{4} (\frac{1}{36})$ .

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Step 1.1.1

Multiply $\frac{1}{4}$ by $\frac{1}{36}$ .

$\frac{1}{4 \cdot 36} + {(- \frac{1}{12})}^{2}$

Step 1.1.2

Multiply $4$ by $36$ .

$\frac{1}{144} + {(- \frac{1}{12})}^{2}$

Step 1.2

Use the power rule ${(a b)}^{n} = a^{n} b^{n}$ to distribute the exponent.

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Step 1.2.1

Apply the product rule to $- \frac{1}{12}$ .

$\frac{1}{144} + {(- 1)}^{2} {(\frac{1}{12})}^{2}$

Step 1.2.2

Apply the product rule to $\frac{1}{12}$ .

$\frac{1}{144} + {(- 1)}^{2} \frac{1^{2}}{12^{2}}$

Step 1.3

Raise $- 1$ to the power of $2$ .

$\frac{1}{144} + 1 \frac{1^{2}}{12^{2}}$

Step 1.4

Multiply $\frac{1^{2}}{12^{2}}$ by $1$ .

$\frac{1}{144} + \frac{1^{2}}{12^{2}}$

Step 1.5

One to any power is one.

$\frac{1}{144} + \frac{1}{12^{2}}$

Step 1.6

Raise $12$ to the power of $2$ .

$\frac{1}{144} + \frac{1}{144}$

Step 2

Simplify terms.

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Step 2.1

Combine the numerators over the common denominator.

$\frac{1 + 1}{144}$

Step 2.2

Add $1$ and $1$ .

$\frac{2}{144}$

Step 2.3

Cancel the common factor of $2$ and $144$ .

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Step 2.3.1

Factor $2$ out of $2$ .

$\frac{2 (1)}{144}$

Step 2.3.2

Cancel the common factors.

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Step 2.3.2.1

Factor $2$ out of $144$ .

$\frac{2 \cdot 1}{2 \cdot 72}$

Step 2.3.2.2

Cancel the common factor.

$\frac{2 \cdot 1}{2 \cdot 72}$

Step 2.3.2.3

Rewrite the expression.

$\frac{1}{72}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$\frac{1}{72}$

Decimal Form:

$0.013\overline{8}$