Evaluate (-1/8)^2-18

${(- \frac{1}{8})}^{2} - 18$

Step 1

Simplify each term.

Use the power rule ${(a b)}^{n} = a^{n} b^{n}$ to distribute the exponent.

Apply the product rule to $- \frac{1}{8}$ .

${(- 1)}^{2} {(\frac{1}{8})}^{2} - 18$

Apply the product rule to $\frac{1}{8}$ .

${(- 1)}^{2} \frac{1^{2}}{8^{2}} - 18$

Raise $- 1$ to the power of $2$ .

$1 \frac{1^{2}}{8^{2}} - 18$

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

$\frac{1^{2}}{8^{2}} - 18$

One to any power is one.

$\frac{1}{8^{2}} - 18$

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

$\frac{1}{64} - 18$

Step 2

To write $- 18$ as a fraction with a common denominator, multiply by $\frac{64}{64}$ .

$\frac{1}{64} - 18 \cdot \frac{64}{64}$

Step 3

Combine $- 18$ and $\frac{64}{64}$ .

$\frac{1}{64} + \frac{- 18 \cdot 64}{64}$

Step 4

Combine the numerators over the common denominator.

$\frac{1 - 18 \cdot 64}{64}$

Step 5

Simplify the numerator.

Multiply $- 18$ by $64$ .

$\frac{1 - 1152}{64}$

Subtract $1152$ from $1$ .

$\frac{- 1151}{64}$

Step 6

Move the negative in front of the fraction.

$- \frac{1151}{64}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$- \frac{1151}{64}$

Decimal Form:

$- 17.984375$

Mixed Number Form:

$- 17 \frac{63}{64}$