Algebra Examples

$2^{2} - - 3^{- 2}$

Step 1

Replace all occurrences of $-$ $-$ with a single $+$ . Two consecutive minus signs have the same mathematical meaning as a single plus sign because $- 1 \cdot - 1 = 1$

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

Step 2

Simplify each term.

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Step 2.1

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

$4 + 3^{- 2}$

Step 2.2

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

$4 + \frac{1}{3^{2}}$

Step 2.3

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

$4 + \frac{1}{9}$

Step 3

To write $4$ as a fraction with a common denominator, multiply by $\frac{9}{9}$ .

$4 \cdot \frac{9}{9} + \frac{1}{9}$

Step 4

Combine $4$ and $\frac{9}{9}$ .

$\frac{4 \cdot 9}{9} + \frac{1}{9}$

Step 5

Combine the numerators over the common denominator.

$\frac{4 \cdot 9 + 1}{9}$

Step 6

Simplify the numerator.

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Step 6.1

Multiply $4$ by $9$ .

$\frac{36 + 1}{9}$

Step 6.2

Add $36$ and $1$ .

$\frac{37}{9}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$\frac{37}{9}$

Decimal Form:

$4.\overline{1}$

Mixed Number Form:

$4 \frac{1}{9}$