Simplify - cube root of 2x^4y^2*3 cube root of 20x^5y

$- \sqrt[3]{2 x^{4} y^{2}} \cdot 3 \sqrt[3]{20 x^{5} y}$

Step 1

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

Factor out $x^{3}$ .

$- \sqrt[3]{2 (x^{3} x) y^{2}} \cdot (3 \sqrt[3]{20 x^{5} y})$

Reorder $2$ and $x^{3}$ .

$- \sqrt[3]{x^{3} \cdot 2 x y^{2}} \cdot (3 \sqrt[3]{20 x^{5} y})$

Add parentheses.

$- \sqrt[3]{x^{3} \cdot 2 (x y^{2})} \cdot (3 \sqrt[3]{20 x^{5} y})$

Add parentheses.

$- \sqrt[3]{x^{3} \cdot (2 x y^{2})} \cdot (3 \sqrt[3]{20 x^{5} y})$

Step 2

Pull terms out from under the radical.

$- (x \sqrt[3]{2 x y^{2}}) \cdot (3 \sqrt[3]{20 x^{5} y})$

Step 3

Rewrite $20 x^{5} y$ as $x^{3} \cdot (20 x^{2} y)$ .

Factor out $x^{3}$ .

$- x \sqrt[3]{2 x y^{2}} \cdot (3 \sqrt[3]{20 (x^{3} x^{2}) y})$

Reorder $20$ and $x^{3}$ .

$- x \sqrt[3]{2 x y^{2}} \cdot (3 \sqrt[3]{x^{3} \cdot 20 x^{2} y})$

Add parentheses.

$- x \sqrt[3]{2 x y^{2}} \cdot (3 \sqrt[3]{x^{3} \cdot 20 (x^{2} y)})$

Add parentheses.

$- x \sqrt[3]{2 x y^{2}} \cdot (3 \sqrt[3]{x^{3} \cdot (20 x^{2} y)})$

Step 4

Pull terms out from under the radical.

$- x \sqrt[3]{2 x y^{2}} \cdot (3 (x \sqrt[3]{20 x^{2} y}))$

Step 5

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

Move $x$ .

$- (x \cdot x) \sqrt[3]{2 x y^{2}} \cdot (3 (\sqrt[3]{20 x^{2} y}))$

Multiply $x$ by $x$ .

$- x^{2} \sqrt[3]{2 x y^{2}} \cdot (3 (\sqrt[3]{20 x^{2} y}))$

Step 6

Multiply $- x^{2} \sqrt[3]{2 x y^{2}} (3 \sqrt[3]{20 x^{2} y})$ .

Multiply $3$ by $- 1$ .

$- 3 x^{2} \sqrt[3]{2 x y^{2}} \sqrt[3]{20 x^{2} y}$

Combine using the product rule for radicals.

$- 3 x^{2} \sqrt[3]{20 x^{2} y (2 x y^{2})}$

Multiply $2$ by $20$ .

$- 3 x^{2} \sqrt[3]{40 x^{2} y (x y^{2})}$

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

$- 3 x^{2} \sqrt[3]{40 (x^{1} x^{2}) y \cdot y^{2}}$

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

$- 3 x^{2} \sqrt[3]{40 x^{1 + 2} y \cdot y^{2}}$

Add $1$ and $2$ .

$- 3 x^{2} \sqrt[3]{40 x^{3} y \cdot y^{2}}$

Multiply $y$ by $y^{2}$ by adding the exponents.

Move $y^{2}$ .

$- 3 x^{2} \sqrt[3]{40 x^{3} (y^{2} y)}$

Multiply $y^{2}$ by $y$ .

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

$- 3 x^{2} \sqrt[3]{40 x^{3} (y^{2} y^{1})}$

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

$- 3 x^{2} \sqrt[3]{40 x^{3} y^{2 + 1}}$

Add $2$ and $1$ .

$- 3 x^{2} \sqrt[3]{40 x^{3} y^{3}}$

Step 7

Rewrite $40 x^{3} y^{3}$ as ${(2 x y)}^{3} \cdot 5$ .

Factor $8$ out of $40$ .

$- 3 x^{2} \sqrt[3]{8 (5) x^{3} y^{3}}$

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

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

Move $5$ .

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

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

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

Step 8

Pull terms out from under the radical.

$- 3 x^{2} (2 x y \sqrt[3]{5})$

Step 9

Multiply $x^{2}$ by $x$ by adding the exponents.

Move $x$ .

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

Multiply $x$ by $x^{2}$ .

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

$- 3 (x^{1} x^{2}) (2 y \sqrt[3]{5})$

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

$- 3 x^{1 + 2} (2 y \sqrt[3]{5})$

Add $1$ and $2$ .

$- 3 x^{3} (2 y \sqrt[3]{5})$

Step 10

Multiply $2$ by $- 3$ .

$- 6 x^{3} y \sqrt[3]{5}$

Simplify - cube root of 2x^4y^2*3 cube root of 20x^5y

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