Simplify 6 cube root of -16+2/3 cube root of -54-5 cube root of 250

$6 \sqrt[3]{- 16} + \frac{2}{3} \sqrt[3]{- 54} - 5 \sqrt[3]{250}$

Simplify each term.

Rewrite $- 16$ as ${(- 2)}^{3} \cdot 2$ .

Factor $- 8$ out of $- 16$ .

$6 \sqrt[3]{- 8 (2)} + \frac{2}{3} \cdot \sqrt[3]{- 54} - 5 \sqrt[3]{250}$

Rewrite $- 8$ as ${(- 2)}^{3}$ .

$6 \sqrt[3]{{(- 2)}^{3} \cdot 2} + \frac{2}{3} \cdot \sqrt[3]{- 54} - 5 \sqrt[3]{250}$

Pull terms out from under the radical.

$6 (- 2 \sqrt[3]{2}) + \frac{2}{3} \cdot \sqrt[3]{- 54} - 5 \sqrt[3]{250}$

Multiply $- 2$ by $6$ .

$- 12 \sqrt[3]{2} + \frac{2}{3} \cdot \sqrt[3]{- 54} - 5 \sqrt[3]{250}$

Rewrite $- 54$ as ${(- 3)}^{3} \cdot 2$ .

Factor $- 27$ out of $- 54$ .

$- 12 \sqrt[3]{2} + \frac{2}{3} \cdot \sqrt[3]{- 27 (2)} - 5 \sqrt[3]{250}$

Rewrite $- 27$ as ${(- 3)}^{3}$ .

$- 12 \sqrt[3]{2} + \frac{2}{3} \cdot \sqrt[3]{{(- 3)}^{3} \cdot 2} - 5 \sqrt[3]{250}$

Pull terms out from under the radical.

$- 12 \sqrt[3]{2} + \frac{2}{3} \cdot (- 3 \sqrt[3]{2}) - 5 \sqrt[3]{250}$

Cancel the common factor of $3$ .

Factor $3$ out of $- 3 \sqrt[3]{2}$ .

$- 12 \sqrt[3]{2} + \frac{2}{3} \cdot (3 (- \sqrt[3]{2})) - 5 \sqrt[3]{250}$

Cancel the common factor.

$- 12 \sqrt[3]{2} + \frac{2}{3} \cdot (3 (- \sqrt[3]{2})) - 5 \sqrt[3]{250}$

Rewrite the expression.

$- 12 \sqrt[3]{2} + 2 \cdot (- \sqrt[3]{2}) - 5 \sqrt[3]{250}$

Multiply $- 1$ by $2$ .

$- 12 \sqrt[3]{2} - 2 \cdot \sqrt[3]{2} - 5 \sqrt[3]{250}$

Rewrite $250$ as $5^{3} \cdot 2$ .

Factor $125$ out of $250$ .

$- 12 \sqrt[3]{2} - 2 \sqrt[3]{2} - 5 \sqrt[3]{125 (2)}$

Rewrite $125$ as $5^{3}$ .

$- 12 \sqrt[3]{2} - 2 \sqrt[3]{2} - 5 \sqrt[3]{5^{3} \cdot 2}$

Pull terms out from under the radical.

$- 12 \sqrt[3]{2} - 2 \sqrt[3]{2} - 5 (5 \sqrt[3]{2})$

Multiply $5$ by $- 5$ .

$- 12 \sqrt[3]{2} - 2 \sqrt[3]{2} - 25 \sqrt[3]{2}$

Simplify by adding terms.

Subtract $2 \sqrt[3]{2}$ from $- 12 \sqrt[3]{2}$ .

$- 14 \sqrt[3]{2} - 25 \sqrt[3]{2}$

Subtract $25 \sqrt[3]{2}$ from $- 14 \sqrt[3]{2}$ .

$- 39 \sqrt[3]{2}$

The result can be shown in multiple forms.

Exact Form:

$- 39 \sqrt[3]{2}$

Decimal Form:

$- 49.13692094 \dots$

Simplify 6 cube root of -16+2/3 cube root of -54-5 cube root of 250

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