Evaluate (4^-2-8^-1)/(4^-2+8^-1)

$\frac{4^{- 2} - 8^{- 1}}{4^{- 2} + 8^{- 1}}$

Simplify the numerator.

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

$\frac{\frac{1}{4^{2}} - 8^{- 1}}{4^{- 2} + 8^{- 1}}$

Raise $4$ to the power of $2$ .

$\frac{\frac{1}{16} - 8^{- 1}}{4^{- 2} + 8^{- 1}}$

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

$\frac{\frac{1}{16} - \frac{1}{8}}{4^{- 2} + 8^{- 1}}$

To write $- \frac{1}{8}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{\frac{1}{16} - \frac{1}{8} \cdot \frac{2}{2}}{4^{- 2} + 8^{- 1}}$

Write each expression with a common denominator of $16$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{1}{8}$ by $\frac{2}{2}$ .

$\frac{\frac{1}{16} - \frac{2}{8 \cdot 2}}{4^{- 2} + 8^{- 1}}$

Multiply $8$ by $2$ .

$\frac{\frac{1}{16} - \frac{2}{16}}{4^{- 2} + 8^{- 1}}$

Combine the numerators over the common denominator.

$\frac{\frac{1 - 2}{16}}{4^{- 2} + 8^{- 1}}$

Subtract $2$ from $1$ .

$\frac{\frac{- 1}{16}}{4^{- 2} + 8^{- 1}}$

Move the negative in front of the fraction.

$\frac{- \frac{1}{16}}{4^{- 2} + 8^{- 1}}$

Simplify the denominator.

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

$\frac{- \frac{1}{16}}{\frac{1}{4^{2}} + 8^{- 1}}$

Raise $4$ to the power of $2$ .

$\frac{- \frac{1}{16}}{\frac{1}{16} + 8^{- 1}}$

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

$\frac{- \frac{1}{16}}{\frac{1}{16} + \frac{1}{8}}$

To write $\frac{1}{8}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{- \frac{1}{16}}{\frac{1}{16} + \frac{1}{8} \cdot \frac{2}{2}}$

Write each expression with a common denominator of $16$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{1}{8}$ by $\frac{2}{2}$ .

$\frac{- \frac{1}{16}}{\frac{1}{16} + \frac{2}{8 \cdot 2}}$

Multiply $8$ by $2$ .

$\frac{- \frac{1}{16}}{\frac{1}{16} + \frac{2}{16}}$

Combine the numerators over the common denominator.

$\frac{- \frac{1}{16}}{\frac{1 + 2}{16}}$

Add $1$ and $2$ .

$\frac{- \frac{1}{16}}{\frac{3}{16}}$

Multiply the numerator by the reciprocal of the denominator.

$- \frac{1}{16} \cdot \frac{16}{3}$

Cancel the common factor of $16$ .

Move the leading negative in $- \frac{1}{16}$ into the numerator.

$\frac{- 1}{16} \cdot \frac{16}{3}$

Cancel the common factor.

$\frac{- 1}{16} \cdot \frac{16}{3}$

Rewrite the expression.

$- \frac{1}{3}$

The result can be shown in multiple forms.

Exact Form:

$- \frac{1}{3}$

Decimal Form:

$- 0.\overline{3}$

Evaluate (4^-2-8^-1)/(4^-2+8^-1)

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