Simplify -2 fourth root of 80x^8y^9z

$- 2 \sqrt[4]{80 x^{8} y^{9} z}$

Rewrite $80 x^{8} y^{9} z$ as ${(2 x^{2} y^{2})}^{4} \cdot (5 y z)$ .

Factor $16$ out of $80$ .

$- 2 \sqrt[4]{16 (5) x^{8} y^{9} z}$

Rewrite $16$ as $2^{4}$ .

$- 2 \sqrt[4]{2^{4} \cdot 5 x^{8} y^{9} z}$

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

$- 2 \sqrt[4]{2^{4} \cdot 5 {(x^{2})}^{4} y^{9} z}$

Factor out $y^{8}$ .

$- 2 \sqrt[4]{2^{4} \cdot 5 {(x^{2})}^{4} (y^{8} y) z}$

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

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

Move $5$ .

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

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

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

Add parentheses.

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

Add parentheses.

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

Pull terms out from under the radical.

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

Multiply $2$ by $- 2$ .

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