Linear Algebra Examples

$7^{3} \sqrt{- 64}$

Step 1

Rewrite $- 64$ as $- 1 (64)$ .

$7^{3} \sqrt{- 1 (64)}$

Step 2

Rewrite $\sqrt{- 1 (64)}$ as $\sqrt{- 1} \cdot \sqrt{64}$ .

$7^{3} (\sqrt{- 1} \cdot \sqrt{64})$

Step 3

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

$7^{3} (i \cdot \sqrt{64})$

Step 4

Raise $7$ to the power of $3$ .

$343 (i \cdot \sqrt{64})$

Step 5

Rewrite $64$ as $8^{2}$ .

$343 (i \cdot \sqrt{8^{2}})$

Step 6

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

$343 (i \cdot 8)$

Step 7

Move $8$ to the left of $i$ .

$343 (8 \cdot i)$

Step 8

Multiply $8$ by $343$ .

$2744 i$