Simplify the Radical Expression cube root of 9xy^2*3 cube root of 3x^4y^6

$\sqrt[3]{9 x y^{2}} \cdot 3 \sqrt[3]{3 x^{4} y^{6}}$

Step 1

Move $3$ to the left of $\sqrt[3]{9 x y^{2}}$ .

$3 \cdot \sqrt[3]{9 x y^{2}} \sqrt[3]{3 x^{4} y^{6}}$

Step 2

Rewrite $3 x^{4} y^{6}$ as ${(x y^{2})}^{3} \cdot (3 x)$ .

Factor out $x^{3}$ .

$3 \sqrt[3]{9 x y^{2}} \sqrt[3]{3 (x^{3} x) y^{6}}$

Rewrite $y^{6}$ as ${(y^{2})}^{3}$ .

$3 \sqrt[3]{9 x y^{2}} \sqrt[3]{3 (x^{3} x) {(y^{2})}^{3}}$

Move $x$ .

$3 \sqrt[3]{9 x y^{2}} \sqrt[3]{3 (x^{3}) {(y^{2})}^{3} x}$

Move $3$ .

$3 \sqrt[3]{9 x y^{2}} \sqrt[3]{x^{3} {(y^{2})}^{3} \cdot 3 x}$

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

$3 \sqrt[3]{9 x y^{2}} \sqrt[3]{{(x y^{2})}^{3} \cdot 3 x}$

Add parentheses.

$3 \sqrt[3]{9 x y^{2}} \sqrt[3]{{(x y^{2})}^{3} \cdot (3 x)}$

Step 3

Pull terms out from under the radical.

$3 \sqrt[3]{9 x y^{2}} (x y^{2} \sqrt[3]{3 x})$

Step 4

Multiply $3 \sqrt[3]{9 x y^{2}} (x y^{2} \sqrt[3]{3 x})$ .

Combine using the product rule for radicals.

$3 (x y^{2} \sqrt[3]{9 x y^{2} (3 x)})$

Multiply $3$ by $9$ .

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

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

$3 (x y^{2} \sqrt[3]{27 (x^{1} x) y^{2}})$

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

$3 (x y^{2} \sqrt[3]{27 (x^{1} x^{1}) y^{2}})$

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

$3 (x y^{2} \sqrt[3]{27 x^{1 + 1} y^{2}})$

Add $1$ and $1$ .

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

Step 5

Rewrite $27 x^{2} y^{2}$ as $3^{3} (x^{2} y^{2})$ .

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

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

Add parentheses.

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

Step 6

Pull terms out from under the radical.

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

Step 7

Rewrite using the commutative property of multiplication.

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

Step 8

Multiply $3$ by $3$ .

$9 x y^{2} \sqrt[3]{x^{2} y^{2}}$

Simplify the Radical Expression cube root of 9xy^2*3 cube root of 3x^4y^6

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