Simplify 4 cube root of x-6 cube root of 2+8 cube root of 16-5 cube root of 27x

$4 \sqrt[3]{x} - 6 \sqrt[3]{2} + 8 \sqrt[3]{16} - 5 \sqrt[3]{27 x}$

Simplify each term.

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

Factor $8$ out of $16$ .

$4 \sqrt[3]{x} - 6 \sqrt[3]{2} + 8 \sqrt[3]{8 (2)} - 5 \sqrt[3]{27 x}$

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

$4 \sqrt[3]{x} - 6 \sqrt[3]{2} + 8 \sqrt[3]{2^{3} \cdot 2} - 5 \sqrt[3]{27 x}$

Pull terms out from under the radical.

$4 \sqrt[3]{x} - 6 \sqrt[3]{2} + 8 (2 \sqrt[3]{2}) - 5 \sqrt[3]{27 x}$

Multiply $2$ by $8$ .

$4 \sqrt[3]{x} - 6 \sqrt[3]{2} + 16 \sqrt[3]{2} - 5 \sqrt[3]{27 x}$

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

$4 \sqrt[3]{x} - 6 \sqrt[3]{2} + 16 \sqrt[3]{2} - 5 \sqrt[3]{3^{3} x}$

Pull terms out from under the radical.

$4 \sqrt[3]{x} - 6 \sqrt[3]{2} + 16 \sqrt[3]{2} - 5 (3 \sqrt[3]{x})$

Multiply $3$ by $- 5$ .

$4 \sqrt[3]{x} - 6 \sqrt[3]{2} + 16 \sqrt[3]{2} - 15 \sqrt[3]{x}$

Simplify by adding terms.

Subtract $15 \sqrt[3]{x}$ from $4 \sqrt[3]{x}$ .

$- 11 \sqrt[3]{x} - 6 \sqrt[3]{2} + 16 \sqrt[3]{2}$

Add $- 6 \sqrt[3]{2}$ and $16 \sqrt[3]{2}$ .

$- 11 \sqrt[3]{x} + 10 \sqrt[3]{2}$