Simplify 4 cube root of x^10+5x^3 cube root of 8x

$4 \sqrt[3]{x^{10}} + 5 x^{3} \sqrt[3]{8 x}$

Step 1

Simplify each term.

Rewrite $x^{10}$ as ${(x^{3})}^{3} x$ .

Factor out $x^{9}$ .

$4 \sqrt[3]{x^{9} x} + 5 x^{3} \sqrt[3]{8 x}$

Rewrite $x^{9}$ as ${(x^{3})}^{3}$ .

$4 \sqrt[3]{{(x^{3})}^{3} x} + 5 x^{3} \sqrt[3]{8 x}$

Pull terms out from under the radical.

$4 (x^{3} \sqrt[3]{x}) + 5 x^{3} \sqrt[3]{8 x}$

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

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

Pull terms out from under the radical.

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

Multiply $2$ by $5$ .

$4 x^{3} \sqrt[3]{x} + 10 x^{3} \sqrt[3]{x}$

Step 2

Add $4 x^{3} \sqrt[3]{x}$ and $10 x^{3} \sqrt[3]{x}$ .

$14 x^{3} \sqrt[3]{x}$