Basic Math Examples

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

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

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

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

Step 1.4

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

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

Step 2

Find the common denominator.

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Step 2.1

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

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

Step 2.2

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

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

Step 2.3

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

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

Step 2.4

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

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

Step 2.5

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

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

Step 2.6

Multiply $3$ by $3$ .

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

Step 3

Combine the numerators over the common denominator.

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

Step 4

Simplify by adding numbers.

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Step 4.1

Add $9$ and $3$ .

$\frac{12 + 1}{9}$

Step 4.2

Add $12$ and $1$ .

$\frac{13}{9}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$\frac{13}{9}$

Decimal Form:

$1.\overline{4}$

Mixed Number Form:

$1 \frac{4}{9}$