Pre-Algebra Examples

$16 - (15 - {(- 2)}^{- 3})$

Step 1

Simplify each term.

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Step 1.1

Simplify each term.

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Step 1.1.1

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

$16 - (15 - \frac{1}{{(- 2)}^{3}})$

Step 1.1.2

Raise $- 2$ to the power of $3$ .

$16 - (15 - \frac{1}{- 8})$

Step 1.1.3

Move the negative in front of the fraction.

$16 - (15 - - \frac{1}{8})$

Step 1.1.4

Multiply $- - \frac{1}{8}$ .

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Step 1.1.4.1

Multiply $- 1$ by $- 1$ .

$16 - (15 + 1 (\frac{1}{8}))$

Step 1.1.4.2

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

$16 - (15 + \frac{1}{8})$

Step 1.2

To write $15$ as a fraction with a common denominator, multiply by $\frac{8}{8}$ .

$16 - (15 \cdot \frac{8}{8} + \frac{1}{8})$

Step 1.3

Combine $15$ and $\frac{8}{8}$ .

$16 - (\frac{15 \cdot 8}{8} + \frac{1}{8})$

Step 1.4

Combine the numerators over the common denominator.

$16 - \frac{15 \cdot 8 + 1}{8}$

Step 1.5

Simplify the numerator.

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Step 1.5.1

Multiply $15$ by $8$ .

$16 - \frac{120 + 1}{8}$

Step 1.5.2

Add $120$ and $1$ .

$16 - \frac{121}{8}$

Step 2

To write $16$ as a fraction with a common denominator, multiply by $\frac{8}{8}$ .

$16 \cdot \frac{8}{8} - \frac{121}{8}$

Step 3

Combine $16$ and $\frac{8}{8}$ .

$\frac{16 \cdot 8}{8} - \frac{121}{8}$

Step 4

Combine the numerators over the common denominator.

$\frac{16 \cdot 8 - 121}{8}$

Step 5

Simplify the numerator.

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Step 5.1

Multiply $16$ by $8$ .

$\frac{128 - 121}{8}$

Step 5.2

Subtract $121$ from $128$ .

$\frac{7}{8}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$\frac{7}{8}$

Decimal Form:

$0.875$