Basic Math Examples

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

Step 1

Simplify each term.

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Step 1.1

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

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Step 1.1.1

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

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

Step 1.1.2

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

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

Step 1.2

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

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

Step 1.3

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

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

Step 1.4

One to any power is one.

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

Step 1.5

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

$\frac{1}{9} - (- \frac{1}{3}) - 3 + {(- 3)}^{2}$

Step 1.6

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

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Step 1.6.1

Multiply $- 1$ by $- 1$ .

$\frac{1}{9} + 1 (\frac{1}{3}) - 3 + {(- 3)}^{2}$

Step 1.6.2

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

$\frac{1}{9} + \frac{1}{3} - 3 + {(- 3)}^{2}$

Step 1.7

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

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

Step 2

Find the common denominator.

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Step 2.1

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

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

Step 2.2

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

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

Step 2.3

Write $- 3$ as a fraction with denominator $1$ .

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

Step 2.4

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

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

Step 2.5

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

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

Step 2.6

Write $9$ as a fraction with denominator $1$ .

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

Step 2.7

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

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

Step 2.8

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

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

Step 2.9

Multiply $3$ by $3$ .

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

Step 3

Combine the numerators over the common denominator.

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

Step 4

Simplify each term.

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Step 4.1

Multiply $- 3$ by $9$ .

$\frac{1 + 3 - 27 + 9 \cdot 9}{9}$

Step 4.2

Multiply $9$ by $9$ .

$\frac{1 + 3 - 27 + 81}{9}$

Step 5

Simplify by adding and subtracting.

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Step 5.1

Add $1$ and $3$ .

$\frac{4 - 27 + 81}{9}$

Step 5.2

Subtract $27$ from $4$ .

$\frac{- 23 + 81}{9}$

Step 5.3

Add $- 23$ and $81$ .

$\frac{58}{9}$