Basic Math Examples

$- \frac{2}{5} \cdot {(2)}^{3} + \frac{\sqrt{16}}{\sqrt[3]{- 1000}}$

Step 1

Simplify each term.

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Step 1.1

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

$- \frac{2}{5} \cdot 8 + \frac{\sqrt{16}}{\sqrt[3]{- 1000}}$

Step 1.2

Multiply $- \frac{2}{5} \cdot 8$ .

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Step 1.2.1

Multiply $8$ by $- 1$ .

$- 8 (\frac{2}{5}) + \frac{\sqrt{16}}{\sqrt[3]{- 1000}}$

Step 1.2.2

Combine $- 8$ and $\frac{2}{5}$ .

$\frac{- 8 \cdot 2}{5} + \frac{\sqrt{16}}{\sqrt[3]{- 1000}}$

Step 1.2.3

Multiply $- 8$ by $2$ .

$\frac{- 16}{5} + \frac{\sqrt{16}}{\sqrt[3]{- 1000}}$

Step 1.3

Move the negative in front of the fraction.

$- \frac{16}{5} + \frac{\sqrt{16}}{\sqrt[3]{- 1000}}$

Step 1.4

Simplify the numerator.

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Step 1.4.1

Rewrite $16$ as $4^{2}$ .

$- \frac{16}{5} + \frac{\sqrt{4^{2}}}{\sqrt[3]{- 1000}}$

Step 1.4.2

Pull terms out from under the radical, assuming positive real numbers.

$- \frac{16}{5} + \frac{4}{\sqrt[3]{- 1000}}$

Step 1.5

Simplify the denominator.

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Step 1.5.1

Rewrite $- 1000$ as ${(- 10)}^{3}$ .

$- \frac{16}{5} + \frac{4}{\sqrt[3]{{(- 10)}^{3}}}$

Step 1.5.2

Pull terms out from under the radical, assuming real numbers.

$- \frac{16}{5} + \frac{4}{- 10}$

Step 1.6

Cancel the common factor of $4$ and $- 10$ .

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Step 1.6.1

Factor $2$ out of $4$ .

$- \frac{16}{5} + \frac{2 (2)}{- 10}$

Step 1.6.2

Cancel the common factors.

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Step 1.6.2.1

Factor $2$ out of $- 10$ .

$- \frac{16}{5} + \frac{2 \cdot 2}{2 \cdot - 5}$

Step 1.6.2.2

Cancel the common factor.

$- \frac{16}{5} + \frac{2 \cdot 2}{2 \cdot - 5}$

Step 1.6.2.3

Rewrite the expression.

$- \frac{16}{5} + \frac{2}{- 5}$

Step 1.7

Move the negative in front of the fraction.

$- \frac{16}{5} - \frac{2}{5}$

Step 2

Combine fractions.

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Step 2.1

Combine the numerators over the common denominator.

$\frac{- 16 - 2}{5}$

Step 2.2

Simplify the expression.

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Step 2.2.1

Subtract $2$ from $- 16$ .

$\frac{- 18}{5}$

Step 2.2.2

Move the negative in front of the fraction.

$- \frac{18}{5}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$- \frac{18}{5}$

Decimal Form:

$- 3.6$

Mixed Number Form:

$- 3 \frac{3}{5}$