Simplify (2 cube root of 16x^5+5x cube root of 128x^2)

$(2 \sqrt[3]{16 x^{5}} + 5 x \sqrt[3]{128 x^{2}})$

Remove parentheses.

$2 \sqrt[3]{16 x^{5}} + 5 x \sqrt[3]{128 x^{2}}$

Simplify each term.

Rewrite $16 x^{5}$ as ${(2 x)}^{3} \cdot (2 x^{2})$ .

Factor $8$ out of $16$ .

$2 \sqrt[3]{8 (2) x^{5}} + 5 x \sqrt[3]{128 x^{2}}$

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

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

Factor out $x^{3}$ .

$2 \sqrt[3]{2^{3} \cdot 2 (x^{3} x^{2})} + 5 x \sqrt[3]{128 x^{2}}$

Move $2$ .

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

Rewrite $2^{3} x^{3}$ as ${(2 x)}^{3}$ .

$2 \sqrt[3]{{(2 x)}^{3} \cdot 2 x^{2}} + 5 x \sqrt[3]{128 x^{2}}$

Add parentheses.

$2 \sqrt[3]{{(2 x)}^{3} \cdot (2 x^{2})} + 5 x \sqrt[3]{128 x^{2}}$

Pull terms out from under the radical.

$2 (2 x \sqrt[3]{2 x^{2}}) + 5 x \sqrt[3]{128 x^{2}}$

Multiply $2$ by $2$ .

$4 (x \sqrt[3]{2 x^{2}}) + 5 x \sqrt[3]{128 x^{2}}$

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

Factor $64$ out of $128$ .

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

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

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

Add parentheses.

$4 x \sqrt[3]{2 x^{2}} + 5 x \sqrt[3]{4^{3} \cdot (2 x^{2})}$

Pull terms out from under the radical.

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

Multiply $4$ by $5$ .

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

Add $4 x \sqrt[3]{2 x^{2}}$ and $20 x \sqrt[3]{2 x^{2}}$ .

$24 x \sqrt[3]{2 x^{2}}$