Algebra Examples

${(\sqrt{- 4})}^{3}$

Step 1

Rewrite $- 4$ as $- 1 (4)$ .

${\sqrt{- 1 (4)}}^{3}$

Step 2

Rewrite $\sqrt{- 1 (4)}$ as $\sqrt{- 1} \cdot \sqrt{4}$ .

${(\sqrt{- 1} \cdot \sqrt{4})}^{3}$

Step 3

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

${(i \cdot \sqrt{4})}^{3}$

Step 4

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

${(i \cdot \sqrt{2^{2}})}^{3}$

Step 5

Pull terms out from under the radical, assuming positive real numbers.

${(i \cdot 2)}^{3}$

Step 6

Move $2$ to the left of $i$ .

${(2 \cdot i)}^{3}$

Step 7

Apply the product rule to $2 i$ .

$2^{3} i^{3}$

Step 8

Raise $2$ to the power of $3$ .

$8 i^{3}$

Step 9

Factor out $i^{2}$ .

$8 (i^{2} \cdot i)$

Step 10

Rewrite $i^{2}$ as $- 1$ .

$8 (- 1 \cdot i)$

Step 11

Rewrite $- 1 i$ as $- i$ .

$8 (- i)$

Step 12

Multiply $- 1$ by $8$ .

$- 8 i$