Simplify 2 cube root of 16+ cube root of 54-5 cube root of 128

$2 \sqrt[3]{16} + \sqrt[3]{54} - 5 \sqrt[3]{128}$

Simplify each term.

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

Factor $8$ out of $16$ .

$2 \sqrt[3]{8 (2)} + \sqrt[3]{54} - 5 \sqrt[3]{128}$

Rewrite $8$ as $2^{3}$ .

$2 \sqrt[3]{2^{3} \cdot 2} + \sqrt[3]{54} - 5 \sqrt[3]{128}$

Pull terms out from under the radical.

$2 (2 \sqrt[3]{2}) + \sqrt[3]{54} - 5 \sqrt[3]{128}$

Multiply $2$ by $2$ .

$4 \sqrt[3]{2} + \sqrt[3]{54} - 5 \sqrt[3]{128}$

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

Factor $27$ out of $54$ .

$4 \sqrt[3]{2} + \sqrt[3]{27 (2)} - 5 \sqrt[3]{128}$

Rewrite $27$ as $3^{3}$ .

$4 \sqrt[3]{2} + \sqrt[3]{3^{3} \cdot 2} - 5 \sqrt[3]{128}$

Pull terms out from under the radical.

$4 \sqrt[3]{2} + 3 \sqrt[3]{2} - 5 \sqrt[3]{128}$

Rewrite $128$ as $4^{3} \cdot 2$ .

Factor $64$ out of $128$ .

$4 \sqrt[3]{2} + 3 \sqrt[3]{2} - 5 \sqrt[3]{64 (2)}$

Rewrite $64$ as $4^{3}$ .

$4 \sqrt[3]{2} + 3 \sqrt[3]{2} - 5 \sqrt[3]{4^{3} \cdot 2}$

Pull terms out from under the radical.

$4 \sqrt[3]{2} + 3 \sqrt[3]{2} - 5 (4 \sqrt[3]{2})$

Multiply $4$ by $- 5$ .

$4 \sqrt[3]{2} + 3 \sqrt[3]{2} - 20 \sqrt[3]{2}$

Simplify by adding terms.

Add $4 \sqrt[3]{2}$ and $3 \sqrt[3]{2}$ .

$7 \sqrt[3]{2} - 20 \sqrt[3]{2}$

Subtract $20 \sqrt[3]{2}$ from $7 \sqrt[3]{2}$ .

$- 13 \sqrt[3]{2}$

The result can be shown in multiple forms.

Exact Form:

$- 13 \sqrt[3]{2}$

Decimal Form:

$- 16.37897364 \dots$