Simplify cube root of 6xy^3* cube root of 18x^4y

$\sqrt[3]{6 x y^{3}} \cdot \sqrt[3]{18 x^{4} y}$

Step 1

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

Move $x$ .

$\sqrt[3]{6 y^{3} x} \cdot \sqrt[3]{18 x^{4} y}$

Reorder $6$ and $y^{3}$ .

$\sqrt[3]{y^{3} \cdot 6 x} \cdot \sqrt[3]{18 x^{4} y}$

Add parentheses.

$\sqrt[3]{y^{3} \cdot (6 x)} \cdot \sqrt[3]{18 x^{4} y}$

Step 2

Pull terms out from under the radical.

$y \sqrt[3]{6 x} \cdot \sqrt[3]{18 x^{4} y}$

Step 3

Rewrite $18 x^{4} y$ as $x^{3} \cdot (18 x y)$ .

Factor out $x^{3}$ .

$y \sqrt[3]{6 x} \cdot \sqrt[3]{18 (x^{3} x) y}$

Reorder $18$ and $x^{3}$ .

$y \sqrt[3]{6 x} \cdot \sqrt[3]{x^{3} \cdot 18 x y}$

Add parentheses.

$y \sqrt[3]{6 x} \cdot \sqrt[3]{x^{3} \cdot 18 (x y)}$

Add parentheses.

$y \sqrt[3]{6 x} \cdot \sqrt[3]{x^{3} \cdot (18 x y)}$

Step 4

Pull terms out from under the radical.

$y \sqrt[3]{6 x} \cdot (x \sqrt[3]{18 x y})$

Step 5

Multiply $y \sqrt[3]{6 x} (x \sqrt[3]{18 x y})$ .

Combine using the product rule for radicals.

$y (x \sqrt[3]{6 x (18 x y)})$

Multiply $18$ by $6$ .

$y (x \sqrt[3]{108 x (x y)})$

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

$y (x \sqrt[3]{108 (x^{1} x) y})$

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

$y (x \sqrt[3]{108 (x^{1} x^{1}) y})$

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

$y (x \sqrt[3]{108 x^{1 + 1} y})$

Add $1$ and $1$ .

$y (x \sqrt[3]{108 x^{2} y})$

Step 6

Rewrite $108 x^{2} y$ as $3^{3} \cdot (4 x^{2} y)$ .

Factor $27$ out of $108$ .

$y (x \sqrt[3]{27 (4) x^{2} y})$

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

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

Add parentheses.

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

Add parentheses.

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

Step 7

Pull terms out from under the radical.

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

Step 8

Rewrite using the commutative property of multiplication.

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

Simplify cube root of 6xy^3* cube root of 18x^4y

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