Algebra Examples

$x^{0} + 3^{- 1} - 3^{2}$

Step 1

Simplify each term.

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Step 1.1

Anything raised to $0$ is $1$ .

$1 + 3^{- 1} - 3^{2}$

Step 1.2

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

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

Step 1.3

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

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

Step 1.4

Multiply $- 1$ by $9$ .

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

Step 2

Find the common denominator.

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Step 2.1

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

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

Step 2.2

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

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

Step 2.3

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

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

Step 2.4

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

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

Step 2.5

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

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

Step 2.6

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

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

Step 3

Combine the numerators over the common denominator.

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

Step 4

Simplify the expression.

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Step 4.1

Multiply $- 9$ by $3$ .

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

Step 4.2

Add $3$ and $1$ .

$\frac{4 - 27}{3}$

Step 4.3

Subtract $27$ from $4$ .

$\frac{- 23}{3}$

Step 4.4

Move the negative in front of the fraction.

$- \frac{23}{3}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$- \frac{23}{3}$

Decimal Form:

$- 7.\overline{6}$

Mixed Number Form:

$- 7 \frac{2}{3}$