Simplify fourth root of 36x^3y^2* fourth root of 36xy^2

$\sqrt[4]{36 x^{3} y^{2}} \cdot \sqrt[4]{36 x y^{2}}$

Step 1

Multiply $\sqrt[4]{36 x^{3} y^{2}} \sqrt[4]{36 x y^{2}}$ .

Combine using the product rule for radicals.

$\sqrt[4]{36 x^{3} y^{2} (36 x y^{2})}$

Multiply $36$ by $36$ .

$\sqrt[4]{1296 x^{3} y^{2} (x y^{2})}$

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

$\sqrt[4]{1296 (x^{1} x^{3}) y^{2} y^{2}}$

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

$\sqrt[4]{1296 x^{1 + 3} y^{2} y^{2}}$

Add $1$ and $3$ .

$\sqrt[4]{1296 x^{4} y^{2} y^{2}}$

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

Move $y^{2}$ .

$\sqrt[4]{1296 x^{4} (y^{2} y^{2})}$

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

$\sqrt[4]{1296 x^{4} y^{2 + 2}}$

Add $2$ and $2$ .

$\sqrt[4]{1296 x^{4} y^{4}}$

Step 2

Rewrite $1296 x^{4} y^{4}$ as ${(6 x y)}^{4}$ .

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

Step 3

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

$6 x y$