Algebra Examples

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

Step 1

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

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Step 1.1

Factor $16$ out of $80$ .

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

Step 1.2

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

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

Step 1.3

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

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

Step 1.4

Factor out $y^{8}$ .

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

Step 1.5

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

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

Step 1.6

Move $5$ .

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

Step 1.7

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

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

Step 1.8

Add parentheses.

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

Step 1.9

Add parentheses.

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

Step 2

Pull terms out from under the radical.

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

Step 3

Remove non-negative terms from the absolute value.

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

Step 4

Multiply $2$ by $- 2$ .

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