Simplify 2x cube root of 8x^5+x^2 cube root of 27x^2

$2 x \sqrt[3]{8 x^{5}} + x^{2} \sqrt[3]{27 x^{2}}$

Step 1

Simplify each term.

Rewrite $8 x^{5}$ as ${(2 x)}^{3} x^{2}$ .

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

$2 x \sqrt[3]{2^{3} x^{5}} + x^{2} \sqrt[3]{27 x^{2}}$

Factor out $x^{3}$ .

$2 x \sqrt[3]{2^{3} (x^{3} x^{2})} + x^{2} \sqrt[3]{27 x^{2}}$

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

$2 x \sqrt[3]{{(2 x)}^{3} x^{2}} + x^{2} \sqrt[3]{27 x^{2}}$

Pull terms out from under the radical.

$2 x (2 x \sqrt[3]{x^{2}}) + x^{2} \sqrt[3]{27 x^{2}}$

Multiply $x$ by $x$ by adding the exponents.

Move $x$ .

$2 (x \cdot x) (2 \sqrt[3]{x^{2}}) + x^{2} \sqrt[3]{27 x^{2}}$

Multiply $x$ by $x$ .

$2 x^{2} (2 \sqrt[3]{x^{2}}) + x^{2} \sqrt[3]{27 x^{2}}$

Multiply $2$ by $2$ .

$4 x^{2} \sqrt[3]{x^{2}} + x^{2} \sqrt[3]{27 x^{2}}$

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

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

Pull terms out from under the radical.

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

Rewrite using the commutative property of multiplication.

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

Step 2

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

$7 x^{2} \sqrt[3]{x^{2}}$