Simplify cube root of 8x^2y^3z^4

$\sqrt[3]{8 x^{2} y^{3} z^{4}}$

Rewrite $8 x^{2} y^{3} z^{4}$ as ${(2 y z)}^{3} (x^{2} z)$ .

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Rewrite $8$ as $2^{3}$ .

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

Factor out $z^{3}$ .

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

Move $x^{2}$ .

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

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

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

Add parentheses.

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

Pull terms out from under the radical.

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

Simplify cube root of 8x^2y^3z^4

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