Algebra Examples

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

Step 1

Remove parentheses.

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

Step 2

Simplify each term.

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Step 2.1

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

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Step 2.1.1

Factor $8$ out of $16$ .

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

Step 2.1.2

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

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

Step 2.1.3

Factor out $x^{3}$ .

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

Step 2.1.4

Move $2$ .

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

Step 2.1.5

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

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

Step 2.1.6

Add parentheses.

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

Step 2.2

Pull terms out from under the radical.

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

Step 2.3

Multiply $2$ by $2$ .

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

Step 2.4

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

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Step 2.4.1

Factor $64$ out of $128$ .

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

Step 2.4.2

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

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

Step 2.4.3

Add parentheses.

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

Step 2.5

Pull terms out from under the radical.

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

Step 2.6

Multiply $4$ by $5$ .

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

Step 3

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

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