Algebra Examples

$\sqrt{- 16 x^{2} y^{8}}$

Step 1

Rewrite $- 16 x^{2} y^{8}$ as ${(4 x y^{4})}^{2} \cdot - 1$ .

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Step 1.1

Factor $16$ out of $- 16$ .

$\sqrt{16 (- 1) x^{2} y^{8}}$

Step 1.2

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

$\sqrt{4^{2} \cdot - 1 x^{2} y^{8}}$

Step 1.3

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

$\sqrt{4^{2} \cdot - 1 x^{2} {(y^{4})}^{2}}$

Step 1.4

Move $- 1$ .

$\sqrt{4^{2} x^{2} {(y^{4})}^{2} \cdot - 1}$

Step 1.5

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

$\sqrt{{(4 x y^{4})}^{2} \cdot - 1}$

Step 2

Pull terms out from under the radical.

$| 4 x y^{4} | \sqrt{- 1}$

Step 3

Rewrite $\sqrt{- 1}$ as $i$ .

$| 4 x y^{4} | i$

Step 4

Remove non-negative terms from the absolute value.

$4 y^{4} | x | i$

Step 5

Reorder factors in $4 y^{4} | x | i$ .

$4 y^{4} i | x |$