Simplify cube root of x to the power of five y to the power of five

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

Should be rewritten $x^{5} y^{5}$ as ${(x y)}^{3} (x^{2} y^{2})$ .

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Factor out $x^{3}$ .

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

Factor out $y^{3}$ .

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

Put $x^{2}$ .

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

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

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

Add brackets.

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

Withdraw terms from under the radical.

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

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