Calculus Examples

$16 (- 4) - \frac{1}{3} \cdot {(- 4)}^{3}$

Step 1

Simplify each term.

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Step 1.1

Multiply $16$ by $- 4$ .

$- 64 - \frac{1}{3} \cdot {(- 4)}^{3}$

Step 1.2

Raise $- 4$ to the power of $3$ .

$- 64 - \frac{1}{3} \cdot - 64$

Step 1.3

Multiply $- \frac{1}{3} \cdot - 64$ .

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Step 1.3.1

Multiply $- 64$ by $- 1$ .

$- 64 + 64 (\frac{1}{3})$

Step 1.3.2

Combine $64$ and $\frac{1}{3}$ .

$- 64 + \frac{64}{3}$

Step 2

To write $- 64$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$- 64 \cdot \frac{3}{3} + \frac{64}{3}$

Step 3

Combine $- 64$ and $\frac{3}{3}$ .

$\frac{- 64 \cdot 3}{3} + \frac{64}{3}$

Step 4

Combine the numerators over the common denominator.

$\frac{- 64 \cdot 3 + 64}{3}$

Step 5

Simplify the numerator.

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Step 5.1

Multiply $- 64$ by $3$ .

$\frac{- 192 + 64}{3}$

Step 5.2

Add $- 192$ and $64$ .

$\frac{- 128}{3}$

Step 6

Move the negative in front of the fraction.

$- \frac{128}{3}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$- \frac{128}{3}$

Decimal Form:

$- 42.\overline{6}$

Mixed Number Form:

$- 42 \frac{2}{3}$