Basic Math Examples

$\frac{1}{3} - {(\frac{1}{3})}^{2} + {(\frac{1}{3})}^{3}$

Step 1

Find the common denominator.

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Step 1.1

Write $- {(\frac{1}{3})}^{2}$ as a fraction with denominator $1$ .

$\frac{1}{3} + \frac{- {(\frac{1}{3})}^{2}}{1} + {(\frac{1}{3})}^{3}$

Step 1.2

Multiply $\frac{- {(\frac{1}{3})}^{2}}{1}$ by $\frac{3}{3}$ .

$\frac{1}{3} + \frac{- {(\frac{1}{3})}^{2}}{1} \cdot \frac{3}{3} + {(\frac{1}{3})}^{3}$

Step 1.3

Multiply $\frac{- {(\frac{1}{3})}^{2}}{1}$ by $\frac{3}{3}$ .

$\frac{1}{3} + \frac{- {(\frac{1}{3})}^{2} \cdot 3}{3} + {(\frac{1}{3})}^{3}$

Step 1.4

Write ${(\frac{1}{3})}^{3}$ as a fraction with denominator $1$ .

$\frac{1}{3} + \frac{- {(\frac{1}{3})}^{2} \cdot 3}{3} + \frac{{(\frac{1}{3})}^{3}}{1}$

Step 1.5

Multiply $\frac{{(\frac{1}{3})}^{3}}{1}$ by $\frac{3}{3}$ .

$\frac{1}{3} + \frac{- {(\frac{1}{3})}^{2} \cdot 3}{3} + \frac{{(\frac{1}{3})}^{3}}{1} \cdot \frac{3}{3}$

Step 1.6

Multiply $\frac{{(\frac{1}{3})}^{3}}{1}$ by $\frac{3}{3}$ .

$\frac{1}{3} + \frac{- {(\frac{1}{3})}^{2} \cdot 3}{3} + \frac{{(\frac{1}{3})}^{3} \cdot 3}{3}$

Step 2

Combine the numerators over the common denominator.

$\frac{1 - {(\frac{1}{3})}^{2} \cdot 3 + {(\frac{1}{3})}^{3} \cdot 3}{3}$

Step 3

Simplify each term.

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Step 3.1

Apply the product rule to $\frac{1}{3}$ .

$\frac{1 - \frac{1^{2}}{3^{2}} \cdot 3 + {(\frac{1}{3})}^{3} \cdot 3}{3}$

Step 3.2

One to any power is one.

$\frac{1 - \frac{1}{3^{2}} \cdot 3 + {(\frac{1}{3})}^{3} \cdot 3}{3}$

Step 3.3

Raise $3$ to the power of $2$ .

$\frac{1 - \frac{1}{9} \cdot 3 + {(\frac{1}{3})}^{3} \cdot 3}{3}$

Step 3.4

Cancel the common factor of $3$ .

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Step 3.4.1

Move the leading negative in $- \frac{1}{9}$ into the numerator.

$\frac{1 + \frac{- 1}{9} \cdot 3 + {(\frac{1}{3})}^{3} \cdot 3}{3}$

Step 3.4.2

Factor $3$ out of $9$ .

$\frac{1 + \frac{- 1}{3 (3)} \cdot 3 + {(\frac{1}{3})}^{3} \cdot 3}{3}$

Step 3.4.3

Cancel the common factor.

$\frac{1 + \frac{- 1}{3 \cdot 3} \cdot 3 + {(\frac{1}{3})}^{3} \cdot 3}{3}$

Step 3.4.4

Rewrite the expression.

$\frac{1 + \frac{- 1}{3} + {(\frac{1}{3})}^{3} \cdot 3}{3}$

Step 3.5

Move the negative in front of the fraction.

$\frac{1 - \frac{1}{3} + {(\frac{1}{3})}^{3} \cdot 3}{3}$

Step 3.6

Apply the product rule to $\frac{1}{3}$ .

$\frac{1 - \frac{1}{3} + \frac{1^{3}}{3^{3}} \cdot 3}{3}$

Step 3.7

One to any power is one.

$\frac{1 - \frac{1}{3} + \frac{1}{3^{3}} \cdot 3}{3}$

Step 3.8

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

$\frac{1 - \frac{1}{3} + \frac{1}{27} \cdot 3}{3}$

Step 3.9

Cancel the common factor of $3$ .

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Step 3.9.1

Factor $3$ out of $27$ .

$\frac{1 - \frac{1}{3} + \frac{1}{3 (9)} \cdot 3}{3}$

Step 3.9.2

Cancel the common factor.

$\frac{1 - \frac{1}{3} + \frac{1}{3 \cdot 9} \cdot 3}{3}$

Step 3.9.3

Rewrite the expression.

$\frac{1 - \frac{1}{3} + \frac{1}{9}}{3}$

Step 4

Find the common denominator.

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Step 4.1

Write $1$ as a fraction with denominator $1$ .

$\frac{\frac{1}{1} - \frac{1}{3} + \frac{1}{9}}{3}$

Step 4.2

Multiply $\frac{1}{1}$ by $\frac{9}{9}$ .

$\frac{\frac{1}{1} \cdot \frac{9}{9} - \frac{1}{3} + \frac{1}{9}}{3}$

Step 4.3

Multiply $\frac{1}{1}$ by $\frac{9}{9}$ .

$\frac{\frac{9}{9} - \frac{1}{3} + \frac{1}{9}}{3}$

Step 4.4

Multiply $\frac{1}{3}$ by $\frac{3}{3}$ .

$\frac{\frac{9}{9} - (\frac{1}{3} \cdot \frac{3}{3}) + \frac{1}{9}}{3}$

Step 4.5

Multiply $\frac{1}{3}$ by $\frac{3}{3}$ .

$\frac{\frac{9}{9} - \frac{3}{3 \cdot 3} + \frac{1}{9}}{3}$

Step 4.6

Multiply $3$ by $3$ .

$\frac{\frac{9}{9} - \frac{3}{9} + \frac{1}{9}}{3}$

Step 5

Combine the numerators over the common denominator.

$\frac{\frac{9 - 3 + 1}{9}}{3}$

Step 6

Simplify by adding and subtracting.

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Step 6.1

Subtract $3$ from $9$ .

$\frac{\frac{6 + 1}{9}}{3}$

Step 6.2

Add $6$ and $1$ .

$\frac{\frac{7}{9}}{3}$

Step 7

Multiply the numerator by the reciprocal of the denominator.

$\frac{7}{9} \cdot \frac{1}{3}$

Step 8

Multiply $\frac{7}{9} \cdot \frac{1}{3}$ .

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Step 8.1

Multiply $\frac{7}{9}$ by $\frac{1}{3}$ .

$\frac{7}{9 \cdot 3}$

Step 8.2

Multiply $9$ by $3$ .

$\frac{7}{27}$

Step 9

The result can be shown in multiple forms.

Exact Form:

$\frac{7}{27}$

Decimal Form:

$0.\overline{259}$