Simplify 3 cube root of 36xy*2 cube root of 6x^2y^2

$3 \sqrt[3]{36 x y} \cdot 2 \sqrt[3]{6 x^{2} y^{2}}$

Step 1

Multiply $3 \sqrt[3]{36 x y} (2 \sqrt[3]{6 x^{2} y^{2}})$ .

Multiply $2$ by $3$ .

$6 \sqrt[3]{36 x y} \sqrt[3]{6 x^{2} y^{2}}$

Combine using the product rule for radicals.

$6 \sqrt[3]{6 x^{2} y^{2} (36 x y)}$

Multiply $36$ by $6$ .

$6 \sqrt[3]{216 x^{2} y^{2} (x y)}$

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

$6 \sqrt[3]{216 (x^{1} x^{2}) y^{2} y}$

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

$6 \sqrt[3]{216 x^{1 + 2} y^{2} y}$

Add $1$ and $2$ .

$6 \sqrt[3]{216 x^{3} y^{2} y}$

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

$6 \sqrt[3]{216 x^{3} (y^{1} y^{2})}$

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

$6 \sqrt[3]{216 x^{3} y^{1 + 2}}$

Add $1$ and $2$ .

$6 \sqrt[3]{216 x^{3} y^{3}}$

Step 2

Rewrite $216 x^{3} y^{3}$ as ${(6 x y)}^{3}$ .

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

Step 3

Pull terms out from under the radical, assuming real numbers.

$6 (6 x y)$

Step 4

Multiply $6$ by $6$ .

$36 x y$