Combine -z^2 fifth root of 2048z+4 fifth root of 2z^11

$- z^{2} \sqrt[5]{2048 z} + 4 \sqrt[5]{2 z^{11}}$

Simplify each term.

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Rewrite $2048 z$ as $4^{5} \cdot (2 z)$ .

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Factor $1024$ out of $2048$ .

$- z^{2} \sqrt[5]{1024 (2) z} + 4 \sqrt[5]{2 z^{11}}$

Rewrite $1024$ as $4^{5}$ .

$- z^{2} \sqrt[5]{4^{5} \cdot 2 z} + 4 \sqrt[5]{2 z^{11}}$

Add parentheses.

$- z^{2} \sqrt[5]{4^{5} \cdot (2 z)} + 4 \sqrt[5]{2 z^{11}}$

Pull terms out from under the radical.

$- z^{2} (4 \sqrt[5]{2 z}) + 4 \sqrt[5]{2 z^{11}}$

Multiply $4$ by $- 1$ .

$- 4 z^{2} \sqrt[5]{2 z} + 4 \sqrt[5]{2 z^{11}}$

Rewrite $2 z^{11}$ as ${(z^{2})}^{5} \cdot (2 z)$ .

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Factor out $z^{10}$ .

$- 4 z^{2} \sqrt[5]{2 z} + 4 \sqrt[5]{2 (z^{10} z)}$

Rewrite $z^{10}$ as ${(z^{2})}^{5}$ .

$- 4 z^{2} \sqrt[5]{2 z} + 4 \sqrt[5]{2 ({(z^{2})}^{5} z)}$

Reorder $2$ and ${(z^{2})}^{5}$ .

$- 4 z^{2} \sqrt[5]{2 z} + 4 \sqrt[5]{{(z^{2})}^{5} \cdot 2 z}$

Add parentheses.

$- 4 z^{2} \sqrt[5]{2 z} + 4 \sqrt[5]{{(z^{2})}^{5} \cdot (2 z)}$

Pull terms out from under the radical.

$- 4 z^{2} \sqrt[5]{2 z} + 4 z^{2} \sqrt[5]{2 z}$

Add $- 4 z^{2} \sqrt[5]{2 z}$ and $4 z^{2} \sqrt[5]{2 z}$ .

$0$

Combine -z^2 fifth root of 2048z+4 fifth root of 2z^11

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