Simplify cube root of x^3y^16z^2

$\sqrt[3]{x^{3} y^{16} z^{2}}$

Rewrite $x^{3} y^{16} z^{2}$ as ${(x y^{5})}^{3} (y z^{2})$ .

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Factor out $y^{15}$ .

$\sqrt[3]{x^{3} (y^{15} y) z^{2}}$

Rewrite $y^{15}$ as ${(y^{5})}^{3}$ .

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

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

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

Add parentheses.

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

Pull terms out from under the radical.

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

Simplify cube root of x^3y^16z^2

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