Simplify ( square root of -9)(-7 square root of -100)

$(\sqrt{- 9}) (- 7 \sqrt{- 100})$

Rewrite $- 9$ as $- 1 (9)$ .

$\sqrt{- 1 (9)} (- 7 \sqrt{- 100})$

Rewrite $\sqrt{- 1 (9)}$ as $\sqrt{- 1} \cdot \sqrt{9}$ .

$\sqrt{- 1} \cdot \sqrt{9} (- 7 \sqrt{- 100})$

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

$i \cdot \sqrt{9} (- 7 \sqrt{- 100})$

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

$i \cdot \sqrt{9} (- 7 \sqrt{- 1 (100)})$

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

$i \cdot \sqrt{9} (- 7 (\sqrt{- 1} \cdot \sqrt{100}))$

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

$i \cdot \sqrt{9} (- 7 (i \cdot \sqrt{100}))$

Rewrite $9$ as $3^{2}$ .

$i \cdot \sqrt{3^{2}} (- 7 (i \cdot \sqrt{100}))$

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

$i \cdot 3 (- 7 (i \cdot \sqrt{100}))$

Move $3$ to the left of $i$ .

$3 \cdot i (- 7 (i \cdot \sqrt{100}))$

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

$3 i (- 7 (i \cdot \sqrt{10^{2}}))$

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

$3 i (- 7 (i \cdot 10))$

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

$3 i (- 7 (10 \cdot i))$

Multiply $10$ by $- 7$ .

$3 i (- 70 i)$

Multiply $3 i (- 70 i)$ .

Multiply $- 70$ by $3$ .

$- 210 i i$

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

$- 210 (i^{1} i)$

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

$- 210 (i^{1} i^{1})$

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

$- 210 i^{1 + 1}$

Add $1$ and $1$ .

$- 210 i^{2}$

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

$- 210 \cdot - 1$

Multiply $- 210$ by $- 1$ .

$210$