Algebra Examples

$(7 \sqrt{- 16}) (\sqrt{- 81})$

Step 1

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

$7 \sqrt{- 1 (16)} \sqrt{- 81}$

Step 2

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

$7 (\sqrt{- 1} \cdot \sqrt{16}) \sqrt{- 81}$

Step 3

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

$7 (i \cdot \sqrt{16}) \sqrt{- 81}$

Step 4

Rewrite $- 81$ as $- 1 (81)$ .

$7 (i \cdot \sqrt{16}) \sqrt{- 1 (81)}$

Step 5

Rewrite $\sqrt{- 1 (81)}$ as $\sqrt{- 1} \cdot \sqrt{81}$ .

$7 (i \cdot \sqrt{16}) (\sqrt{- 1} \cdot \sqrt{81})$

Step 6

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

$7 (i \cdot \sqrt{16}) (i \cdot \sqrt{81})$

Step 7

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

$7 (i \cdot \sqrt{4^{2}}) (i \cdot \sqrt{81})$

Step 8

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

$7 (i \cdot 4) (i \cdot \sqrt{81})$

Step 9

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

$7 (4 \cdot i) (i \cdot \sqrt{81})$

Step 10

Multiply $4$ by $7$ .

$28 i (i \cdot \sqrt{81})$

Step 11

Rewrite $81$ as $9^{2}$ .

$28 i (i \cdot \sqrt{9^{2}})$

Step 12

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

$28 i (i \cdot 9)$

Step 13

Move $9$ to the left of $i$ .

$28 i (9 \cdot i)$

Step 14

Multiply $28 i (9 i)$ .

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Step 14.1

Multiply $9$ by $28$ .

$252 i i$

Step 14.2

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

$252 (i^{1} i)$

Step 14.3

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

$252 (i^{1} i^{1})$

Step 14.4

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

$252 i^{1 + 1}$

Step 14.5

Add $1$ and $1$ .

$252 i^{2}$

Step 15

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

$252 \cdot - 1$

Step 16

Multiply $252$ by $- 1$ .

$- 252$