Simplify cube root of -12x^4y* cube root of 4x^2y^2

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

Step 1

Rewrite $- 12 x^{4} y$ as ${(- x)}^{3} \cdot (12 x y)$ .

Rewrite $- 12$ as $- 1 (12)$ .

$\sqrt[3]{- 1 (12) x^{4} y} \cdot \sqrt[3]{4 x^{2} y^{2}}$

Rewrite $- 1$ as ${(- 1)}^{3}$ .

$\sqrt[3]{{(- 1)}^{3} \cdot 12 x^{4} y} \cdot \sqrt[3]{4 x^{2} y^{2}}$

Factor out $x^{3}$ .

$\sqrt[3]{{(- 1)}^{3} \cdot 12 (x^{3} x) y} \cdot \sqrt[3]{4 x^{2} y^{2}}$

Move $12$ .

$\sqrt[3]{{(- 1)}^{3} x^{3} \cdot 12 x y} \cdot \sqrt[3]{4 x^{2} y^{2}}$

Rewrite ${(- 1)}^{3} x^{3}$ as ${(- x)}^{3}$ .

$\sqrt[3]{{(- x)}^{3} \cdot 12 x y} \cdot \sqrt[3]{4 x^{2} y^{2}}$

Add parentheses.

$\sqrt[3]{{(- x)}^{3} \cdot 12 (x y)} \cdot \sqrt[3]{4 x^{2} y^{2}}$

Add parentheses.

$\sqrt[3]{{(- x)}^{3} \cdot (12 x y)} \cdot \sqrt[3]{4 x^{2} y^{2}}$

Step 2

Pull terms out from under the radical.

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

Step 3

Multiply $- x \sqrt[3]{12 x y} \sqrt[3]{4 x^{2} y^{2}}$ .

Combine using the product rule for radicals.

$- x \sqrt[3]{4 x^{2} y^{2} (12 x y)}$

Multiply $12$ by $4$ .

$- x \sqrt[3]{48 x^{2} y^{2} (x y)}$

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

$- x \sqrt[3]{48 (x^{1} x^{2}) y^{2} y}$

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

$- x \sqrt[3]{48 x^{1 + 2} y^{2} y}$

Add $1$ and $2$ .

$- x \sqrt[3]{48 x^{3} y^{2} y}$

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

$- x \sqrt[3]{48 x^{3} (y^{1} y^{2})}$

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

$- x \sqrt[3]{48 x^{3} y^{1 + 2}}$

Add $1$ and $2$ .

$- x \sqrt[3]{48 x^{3} y^{3}}$

Step 4

Rewrite $48 x^{3} y^{3}$ as ${(2 x y)}^{3} \cdot 6$ .

Factor $8$ out of $48$ .

$- x \sqrt[3]{8 (6) x^{3} y^{3}}$

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

$- x \sqrt[3]{2^{3} \cdot 6 x^{3} y^{3}}$

Move $6$ .

$- x \sqrt[3]{2^{3} x^{3} y^{3} \cdot 6}$

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

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

Step 5

Pull terms out from under the radical.

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

Step 6

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

Move $x$ .

$- (x \cdot x) (2 y \sqrt[3]{6})$

Multiply $x$ by $x$ .

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

Step 7

Multiply $2$ by $- 1$ .

$- 2 x^{2} y \sqrt[3]{6}$

Simplify cube root of -12x^4y* cube root of 4x^2y^2

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