Basic Math Examples

$- y^{2} \sqrt[3]{54 y} + 3 \sqrt[3]{2 y^{7}}$

Step 1

Simplify each term.

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Step 1.1

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

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Step 1.1.1

Factor $27$ out of $54$ .

$- y^{2} \sqrt[3]{27 (2) y} + 3 \sqrt[3]{2 y^{7}}$

Step 1.1.2

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

$- y^{2} \sqrt[3]{3^{3} \cdot 2 y} + 3 \sqrt[3]{2 y^{7}}$

Step 1.1.3

Add parentheses.

$- y^{2} \sqrt[3]{3^{3} \cdot (2 y)} + 3 \sqrt[3]{2 y^{7}}$

Step 1.2

Pull terms out from under the radical.

$- y^{2} (3 \sqrt[3]{2 y}) + 3 \sqrt[3]{2 y^{7}}$

Step 1.3

Multiply $3$ by $- 1$ .

$- 3 y^{2} \sqrt[3]{2 y} + 3 \sqrt[3]{2 y^{7}}$

Step 1.4

Rewrite $2 y^{7}$ as ${(y^{2})}^{3} \cdot (2 y)$ .

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Step 1.4.1

Factor out $y^{6}$ .

$- 3 y^{2} \sqrt[3]{2 y} + 3 \sqrt[3]{2 (y^{6} y)}$

Step 1.4.2

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

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

Step 1.4.3

Reorder $2$ and ${(y^{2})}^{3}$ .

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

Step 1.4.4

Add parentheses.

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

Step 1.5

Pull terms out from under the radical.

$- 3 y^{2} \sqrt[3]{2 y} + 3 y^{2} \sqrt[3]{2 y}$

Step 2

Add $- 3 y^{2} \sqrt[3]{2 y}$ and $3 y^{2} \sqrt[3]{2 y}$ .

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