Evaluate ((-2)^-8)/-8-(-5)

$\frac{{(- 2)}^{- 8}}{- 8} - (- 5)$

Step 1

Simplify each term.

Move ${(- 2)}^{- 8}$ to the denominator using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$\frac{1}{- 8 {(- 2)}^{8}} - (- 5)$

Raise $- 2$ to the power of $8$ .

$\frac{1}{- 8 \cdot 256} - (- 5)$

Multiply $- 8$ by $256$ .

$\frac{1}{- 2048} - (- 5)$

Move the negative in front of the fraction.

$- \frac{1}{2048} - (- 5)$

Multiply $- 1$ by $- 5$ .

$- \frac{1}{2048} + 5$

Step 2

To write $5$ as a fraction with a common denominator, multiply by $\frac{2048}{2048}$ .

$- \frac{1}{2048} + 5 \cdot \frac{2048}{2048}$

Step 3

Combine $5$ and $\frac{2048}{2048}$ .

$- \frac{1}{2048} + \frac{5 \cdot 2048}{2048}$

Step 4

Combine the numerators over the common denominator.

$\frac{- 1 + 5 \cdot 2048}{2048}$

Step 5

Simplify the numerator.

Multiply $5$ by $2048$ .

$\frac{- 1 + 10240}{2048}$

Add $- 1$ and $10240$ .

$\frac{10239}{2048}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$\frac{10239}{2048}$

Decimal Form:

$4.99951171 \dots$

Mixed Number Form:

$4 \frac{2047}{2048}$