Algebra Examples

$- 2 \sqrt[4]{405 x^{16} y^{7}}$

Step 1

Rewrite $405 x^{16} y^{7}$ as ${(3 x^{4} y)}^{4} \cdot (5 y^{3})$ .

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Step 1.1

Factor $81$ out of $405$ .

$- 2 \sqrt[4]{81 (5) x^{16} y^{7}}$

Step 1.2

Rewrite $81$ as $3^{4}$ .

$- 2 \sqrt[4]{3^{4} \cdot 5 x^{16} y^{7}}$

Step 1.3

Rewrite $x^{16}$ as ${(x^{4})}^{4}$ .

$- 2 \sqrt[4]{3^{4} \cdot 5 {(x^{4})}^{4} y^{7}}$

Step 1.4

Factor out $y^{4}$ .

$- 2 \sqrt[4]{3^{4} \cdot 5 {(x^{4})}^{4} (y^{4} y^{3})}$

Step 1.5

Move $5$ .

$- 2 \sqrt[4]{3^{4} {(x^{4})}^{4} y^{4} \cdot 5 y^{3}}$

Step 1.6

Rewrite $3^{4} {(x^{4})}^{4} y^{4}$ as ${(3 x^{4} y)}^{4}$ .

$- 2 \sqrt[4]{{(3 x^{4} y)}^{4} \cdot 5 y^{3}}$

Step 1.7

Add parentheses.

$- 2 \sqrt[4]{{(3 x^{4} y)}^{4} \cdot (5 y^{3})}$

Step 2

Pull terms out from under the radical.

$- 2 (| 3 x^{4} y | \sqrt[4]{5 y^{3}})$

Step 3

Remove non-negative terms from the absolute value.

$- 2 (3 x^{4} | y | \sqrt[4]{5 y^{3}})$

Step 4

Multiply $3$ by $- 2$ .

$- 6 x^{4} | y | \sqrt[4]{5 y^{3}}$