Algebra Examples

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

Step 1

Move $3^{- 1}$ to the numerator using the negative exponent rule $\frac{1}{b^{- n}} = b^{n}$ .

$(2^{0} + 3^{- 2}) \cdot 3$

Step 2

Simplify each term.

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Step 2.1

Anything raised to $0$ is $1$ .

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

Step 2.2

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

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

Step 2.3

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

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

Step 3

Reduce the expression by cancelling the common factors.

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Step 3.1

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

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

Step 3.2

Simplify the expression.

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Step 3.2.1

Combine the numerators over the common denominator.

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

Step 3.2.2

Add $9$ and $1$ .

$\frac{10}{9} \cdot 3$

Step 3.3

Cancel the common factor of $3$ .

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Step 3.3.1

Factor $3$ out of $9$ .

$\frac{10}{3 (3)} \cdot 3$

Step 3.3.2

Cancel the common factor.

$\frac{10}{3 \cdot 3} \cdot 3$

Step 3.3.3

Rewrite the expression.

$\frac{10}{3}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$\frac{10}{3}$

Decimal Form:

$3.\overline{3}$

Mixed Number Form:

$3 \frac{1}{3}$