Algebra Examples

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

Step 1

Simplify each term.

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Step 1.1

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

$- 1 \cdot 4 + 2^{0} + 2^{- 1}$

Step 1.2

Multiply $- 1$ by $4$ .

$- 4 + 2^{0} + 2^{- 1}$

Step 1.3

Anything raised to $0$ is $1$ .

$- 4 + 1 + 2^{- 1}$

Step 1.4

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

$- 4 + 1 + \frac{1}{2}$

Step 2

Find the common denominator.

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Step 2.1

Write $- 4$ as a fraction with denominator $1$ .

$\frac{- 4}{1} + 1 + \frac{1}{2}$

Step 2.2

Multiply $\frac{- 4}{1}$ by $\frac{2}{2}$ .

$\frac{- 4}{1} \cdot \frac{2}{2} + 1 + \frac{1}{2}$

Step 2.3

Multiply $\frac{- 4}{1}$ by $\frac{2}{2}$ .

$\frac{- 4 \cdot 2}{2} + 1 + \frac{1}{2}$

Step 2.4

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

$\frac{- 4 \cdot 2}{2} + \frac{1}{1} + \frac{1}{2}$

Step 2.5

Multiply $\frac{1}{1}$ by $\frac{2}{2}$ .

$\frac{- 4 \cdot 2}{2} + \frac{1}{1} \cdot \frac{2}{2} + \frac{1}{2}$

Step 2.6

Multiply $\frac{1}{1}$ by $\frac{2}{2}$ .

$\frac{- 4 \cdot 2}{2} + \frac{2}{2} + \frac{1}{2}$

Step 3

Combine the numerators over the common denominator.

$\frac{- 4 \cdot 2 + 2 + 1}{2}$

Step 4

Simplify the expression.

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Step 4.1

Multiply $- 4$ by $2$ .

$\frac{- 8 + 2 + 1}{2}$

Step 4.2

Add $- 8$ and $2$ .

$\frac{- 6 + 1}{2}$

Step 4.3

Add $- 6$ and $1$ .

$\frac{- 5}{2}$

Step 4.4

Move the negative in front of the fraction.

$- \frac{5}{2}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$- \frac{5}{2}$

Decimal Form:

$- 2.5$

Mixed Number Form:

$- 2 \frac{1}{2}$