Pre-Algebra Examples

$3 + {(- 3)}^{- 2} - {(9 + 7)}^{0}$

Step 1

Simplify each term.

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Step 1.1

Rewrite the expression using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$3 + \frac{1}{{(- 3)}^{2}} - {(9 + 7)}^{0}$

Step 1.2

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

$3 + \frac{1}{9} - {(9 + 7)}^{0}$

Step 1.3

Add $9$ and $7$ .

$3 + \frac{1}{9} - 16^{0}$

Step 1.4

Anything raised to $0$ is $1$ .

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

Step 1.5

Multiply $- 1$ by $1$ .

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

Step 2

Find the common denominator.

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Step 2.1

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

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

Step 2.2

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

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

Step 2.3

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

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

Step 2.4

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

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

Step 2.5

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

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

Step 2.6

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

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

Step 3

Combine the numerators over the common denominator.

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

Step 4

Simplify each term.

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Step 4.1

Multiply $3$ by $9$ .

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

Step 4.2

Multiply $- 1$ by $9$ .

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

Step 5

Simplify by adding and subtracting.

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Step 5.1

Add $27$ and $1$ .

$\frac{28 - 9}{9}$

Step 5.2

Subtract $9$ from $28$ .

$\frac{19}{9}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$\frac{19}{9}$

Decimal Form:

$2.\overline{1}$

Mixed Number Form:

$2 \frac{1}{9}$