Algebra Examples

$- \sqrt[3]{2 x^{2} y^{2}} \cdot 2 \sqrt[3]{15 x^{5} y}$

Step 1

Rewrite $15 x^{5} y$ as $x^{3} \cdot (15 x^{2} y)$ .

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Step 1.1

Factor out $x^{3}$ .

$- \sqrt[3]{2 x^{2} y^{2}} \cdot (2 \sqrt[3]{15 (x^{3} x^{2}) y})$

Step 1.2

Reorder $15$ and $x^{3}$ .

$- \sqrt[3]{2 x^{2} y^{2}} \cdot (2 \sqrt[3]{x^{3} \cdot 15 x^{2} y})$

Step 1.3

Add parentheses.

$- \sqrt[3]{2 x^{2} y^{2}} \cdot (2 \sqrt[3]{x^{3} \cdot 15 (x^{2} y)})$

Step 1.4

Add parentheses.

$- \sqrt[3]{2 x^{2} y^{2}} \cdot (2 \sqrt[3]{x^{3} \cdot (15 x^{2} y)})$

Step 2

Pull terms out from under the radical.

$- \sqrt[3]{2 x^{2} y^{2}} \cdot (2 (x \sqrt[3]{15 x^{2} y}))$

Step 3

Multiply $- \sqrt[3]{2 x^{2} y^{2}} (2 x \sqrt[3]{15 x^{2} y})$ .

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Step 3.1

Multiply $2$ by $- 1$ .

$- 2 \sqrt[3]{2 x^{2} y^{2}} (x \sqrt[3]{15 x^{2} y})$

Step 3.2

Combine using the product rule for radicals.

$- 2 (x \sqrt[3]{2 x^{2} y^{2} (15 x^{2} y)})$

Step 3.3

Multiply $15$ by $2$ .

$- 2 (x \sqrt[3]{30 x^{2} y^{2} (x^{2} y)})$

Step 3.4

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$- 2 (x \sqrt[3]{30 x^{2 + 2} y^{2} y})$

Step 3.5

Add $2$ and $2$ .

$- 2 (x \sqrt[3]{30 x^{4} y^{2} y})$

Step 3.6

Raise $y$ to the power of $1$ .

$- 2 (x \sqrt[3]{30 x^{4} (y^{1} y^{2})})$

Step 3.7

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$- 2 (x \sqrt[3]{30 x^{4} y^{1 + 2}})$

Step 3.8

Add $1$ and $2$ .

$- 2 (x \sqrt[3]{30 x^{4} y^{3}})$

Step 4

Rewrite $30 x^{4} y^{3}$ as ${(x y)}^{3} \cdot (30 x)$ .

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Step 4.1

Factor out $x^{3}$ .

$- 2 (x \sqrt[3]{30 (x^{3} x) y^{3}})$

Step 4.2

Move $x$ .

$- 2 (x \sqrt[3]{30 (x^{3}) y^{3} x})$

Step 4.3

Move $30$ .

$- 2 (x \sqrt[3]{(x^{3}) y^{3} \cdot 30 x})$

Step 4.4

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

$- 2 (x \sqrt[3]{{(x y)}^{3} \cdot 30 x})$

Step 4.5

Add parentheses.

$- 2 (x \sqrt[3]{{(x y)}^{3} \cdot (30 x)})$

Step 5

Pull terms out from under the radical.

$- 2 (x (x y \sqrt[3]{30 x}))$

Step 6

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

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Step 6.1

Move $x$ .

$- 2 (x \cdot x (y \sqrt[3]{30 x}))$

Step 6.2

Multiply $x$ by $x$ .

$- 2 (x^{2} (y \sqrt[3]{30 x}))$

Step 7

Reorder factors in $- 2 x^{2} (y \sqrt[3]{30 x})$ .

$- 2 x^{2} y \sqrt[3]{30 x}$