Simplify fourth root of square root of z^5

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Algebra

$\sqrt[4]{\sqrt{z^{5}}}$

Rewrite $z^{5}$ as ${(z^{2})}^{2} z$ .

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Factor out $z^{4}$ .

$\sqrt[4]{\sqrt{z^{4} z}}$

Rewrite $z^{4}$ as ${(z^{2})}^{2}$ .

$\sqrt[4]{\sqrt{{(z^{2})}^{2} z}}$

Pull terms out from under the radical.

$\sqrt[4]{z^{2} \sqrt{z}}$

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