Simplify cube root of x^2y cube root of 16x^4y^2

$\sqrt[3]{x^{2} y} \sqrt[3]{16 x^{4} y^{2}}$

Step 1

Rewrite $16 x^{4} y^{2}$ as ${(2 x)}^{3} \cdot (2 x y^{2})$ .

Factor $8$ out of $16$ .

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

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

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

Factor out $x^{3}$ .

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

Move $2$ .

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

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

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

Add parentheses.

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

Add parentheses.

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

Step 2

Pull terms out from under the radical.

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

Step 3

Rewrite using the commutative property of multiplication.

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

Step 4

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

Combine using the product rule for radicals.

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

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

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

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

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

Add $1$ and $2$ .

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

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

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

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

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

Add $1$ and $2$ .

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

Step 5

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

Move $2$ .

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

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

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

Step 6

Pull terms out from under the radical.

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

Step 7

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

Move $x$ .

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

Multiply $x$ by $x$ .

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

Step 8

Rewrite using the commutative property of multiplication.

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

Simplify cube root of x^2y cube root of 16x^4y^2

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