Trigonometry Examples

$\sqrt[3]{x^{5} y^{5}}$

Step 1

Rewrite $x^{5} y^{5}$ as ${(x y)}^{3} (x^{2} y^{2})$ .

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Step 1.1

Factor out $x^{3}$ .

$\sqrt[3]{x^{3} x^{2} y^{5}}$

Step 1.2

Factor out $y^{3}$ .

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

Step 1.3

Move $x^{2}$ .

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

Step 1.4

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

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

Step 1.5

Add parentheses.

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

Step 2

Pull terms out from under the radical.

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