Algebra Examples

$(3 \sqrt{- 16}) (- 9 \sqrt{- 100})$

Step 1

Rewrite $- 16$ as $- 1 (16)$ .

$3 \sqrt{- 1 (16)} (- 9 \sqrt{- 100})$

Step 2

Rewrite $\sqrt{- 1 (16)}$ as $\sqrt{- 1} \cdot \sqrt{16}$ .

$3 (\sqrt{- 1} \cdot \sqrt{16}) (- 9 \sqrt{- 100})$

Step 3

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

$3 (i \cdot \sqrt{16}) (- 9 \sqrt{- 100})$

Step 4

Rewrite $- 100$ as $- 1 (100)$ .

$3 (i \cdot \sqrt{16}) (- 9 \sqrt{- 1 (100)})$

Step 5

Rewrite $\sqrt{- 1 (100)}$ as $\sqrt{- 1} \cdot \sqrt{100}$ .

$3 (i \cdot \sqrt{16}) (- 9 (\sqrt{- 1} \cdot \sqrt{100}))$

Step 6

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

$3 (i \cdot \sqrt{16}) (- 9 (i \cdot \sqrt{100}))$

Step 7

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

$3 (i \cdot \sqrt{4^{2}}) (- 9 (i \cdot \sqrt{100}))$

Step 8

Pull terms out from under the radical.

$3 (i \cdot | 4 |) (- 9 (i \cdot \sqrt{100}))$

Step 9

The absolute value is the distance between a number and zero. The distance between $0$ and $4$ is $4$ .

$3 (i \cdot 4) (- 9 (i \cdot \sqrt{100}))$

Step 10

Move $4$ to the left of $i$ .

$3 (4 \cdot i) (- 9 (i \cdot \sqrt{100}))$

Step 11

Multiply $4$ by $3$ .

$12 i (- 9 (i \cdot \sqrt{100}))$

Step 12

Rewrite $100$ as $10^{2}$ .

$12 i (- 9 (i \cdot \sqrt{10^{2}}))$

Step 13

Pull terms out from under the radical.

$12 i (- 9 (i \cdot | 10 |))$

Step 14

The absolute value is the distance between a number and zero. The distance between $0$ and $10$ is $10$ .

$12 i (- 9 (i \cdot 10))$

Step 15

Move $10$ to the left of $i$ .

$12 i (- 9 (10 \cdot i))$

Step 16

Multiply $10$ by $- 9$ .

$12 i (- 90 i)$

Step 17

Multiply $12 i (- 90 i)$ .

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Step 17.1

Multiply $- 90$ by $12$ .

$- 1080 i i$

Step 17.2

Raise $i$ to the power of $1$ .

$- 1080 (i^{1} i)$

Step 17.3

Raise $i$ to the power of $1$ .

$- 1080 (i^{1} i^{1})$

Step 17.4

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$- 1080 i^{1 + 1}$

Step 17.5

Add $1$ and $1$ .

$- 1080 i^{2}$

Step 18

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

$- 1080 \cdot - 1$

Step 19

Multiply $- 1080$ by $- 1$ .

$1080$