Algebra Examples

$2 (\sqrt[3]{16 x^{3} y}) + 4 (\sqrt[3]{54 x^{6} y^{5}})$

Step 1

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

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Step 1.1

Factor $8$ out of $16$ .

$2 \sqrt[3]{8 (2) x^{3} y} + 4 (\sqrt[3]{54 x^{6} y^{5}})$

Step 1.2

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

$2 \sqrt[3]{2^{3} \cdot 2 x^{3} y} + 4 (\sqrt[3]{54 x^{6} y^{5}})$

Step 1.3

Move $2$ .

$2 \sqrt[3]{2^{3} x^{3} \cdot 2 y} + 4 (\sqrt[3]{54 x^{6} y^{5}})$

Step 1.4

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

$2 \sqrt[3]{{(2 x)}^{3} \cdot 2 y} + 4 (\sqrt[3]{54 x^{6} y^{5}})$

Step 1.5

Add parentheses.

$2 \sqrt[3]{{(2 x)}^{3} \cdot (2 y)} + 4 (\sqrt[3]{54 x^{6} y^{5}})$

Step 2

Pull terms out from under the radical.

$2 (2 x \sqrt[3]{2 y}) + 4 (\sqrt[3]{54 x^{6} y^{5}})$

Step 3

Multiply $2$ by $2$ .

$4 (x \sqrt[3]{2 y}) + 4 (\sqrt[3]{54 x^{6} y^{5}})$

Step 4

Rewrite $54 x^{6} y^{5}$ as ${(3 x^{2} y)}^{3} \cdot (2 y^{2})$ .

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Step 4.1

Factor $27$ out of $54$ .

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

Step 4.2

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

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

Step 4.3

Rewrite $x^{6}$ as ${(x^{2})}^{3}$ .

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

Step 4.4

Factor out $y^{3}$ .

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

Step 4.5

Move $2$ .

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

Step 4.6

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

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

Step 4.7

Add parentheses.

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

Step 5

Pull terms out from under the radical.

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

Step 6

Multiply $3$ by $4$ .

$4 x \sqrt[3]{2 y} + 12 x^{2} y \sqrt[3]{2 y^{2}}$