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

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

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

Combine using the product rule for radicals.

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

Multiply $36$ by $6$ .

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

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

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

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

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

Add $1$ and $2$ .

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

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

Move $y^{2}$ .

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

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

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

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

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

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

Add $2$ and $1$ .

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

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

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

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

$6 x y$