Simplify (2^-1+2^0)-(6^-1+6^0)

$(2^{- 1} + 2^{0}) - (6^{- 1} + 6^{0})$

Simplify each term.

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

$\frac{1}{2} + 2^{0} - (6^{- 1} + 6^{0})$

Anything raised to $0$ is $1$ .

$\frac{1}{2} + 1 - (6^{- 1} + 6^{0})$

Simplify each term.

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

$\frac{1}{2} + 1 - (\frac{1}{6} + 6^{0})$

Anything raised to $0$ is $1$ .

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

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

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

Combine the numerators over the common denominator.

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

Add $1$ and $6$ .

$\frac{1}{2} + 1 - \frac{7}{6}$

Find the common denominator.

Multiply $\frac{1}{2}$ by $\frac{3}{3}$ .

$\frac{1}{2} \cdot \frac{3}{3} + 1 - \frac{7}{6}$

Multiply $\frac{1}{2}$ by $\frac{3}{3}$ .

$\frac{3}{2 \cdot 3} + 1 - \frac{7}{6}$

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

$\frac{3}{2 \cdot 3} + \frac{1}{1} - \frac{7}{6}$

Multiply $\frac{1}{1}$ by $\frac{6}{6}$ .

$\frac{3}{2 \cdot 3} + \frac{1}{1} \cdot \frac{6}{6} - \frac{7}{6}$

Multiply $\frac{1}{1}$ by $\frac{6}{6}$ .

$\frac{3}{2 \cdot 3} + \frac{6}{6} - \frac{7}{6}$

Multiply $2$ by $3$ .

$\frac{3}{6} + \frac{6}{6} - \frac{7}{6}$

Combine the numerators over the common denominator.

$\frac{3 + 6 - 7}{6}$

Simplify by adding and subtracting.

Add $3$ and $6$ .

$\frac{9 - 7}{6}$

Subtract $7$ from $9$ .

$\frac{2}{6}$

Cancel the common factor of $2$ and $6$ .

Factor $2$ out of $2$ .

$\frac{2 (1)}{6}$

Cancel the common factors.

Factor $2$ out of $6$ .

$\frac{2 \cdot 1}{2 \cdot 3}$

Cancel the common factor.

$\frac{2 \cdot 1}{2 \cdot 3}$

Rewrite the expression.

$\frac{1}{3}$

The result can be shown in multiple forms.

Exact Form:

$\frac{1}{3}$

Decimal Form:

$0.\overline{3}$

Simplify (2^-1+2^0)-(6^-1+6^0)

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