Simplify (-2 square root of -49)(5 square root of -100)

$(- 2 \sqrt{- 49}) (5 \sqrt{- 100})$

Rewrite $- 49$ as $- 1 (49)$ .

$- 2 \sqrt{- 1 (49)} (5 \sqrt{- 100})$

Rewrite $\sqrt{- 1 (49)}$ as $\sqrt{- 1} \cdot \sqrt{49}$ .

$- 2 (\sqrt{- 1} \cdot \sqrt{49}) (5 \sqrt{- 100})$

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

$- 2 (i \cdot \sqrt{49}) (5 \sqrt{- 100})$

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

$- 2 (i \cdot \sqrt{49}) (5 \sqrt{- 1 (100)})$

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

$- 2 (i \cdot \sqrt{49}) (5 (\sqrt{- 1} \cdot \sqrt{100}))$

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

$- 2 (i \cdot \sqrt{49}) (5 (i \cdot \sqrt{100}))$

Rewrite $49$ as $7^{2}$ .

$- 2 (i \cdot \sqrt{7^{2}}) (5 (i \cdot \sqrt{100}))$

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

$- 2 (i \cdot 7) (5 (i \cdot \sqrt{100}))$

Move $7$ to the left of $i$ .

$- 2 (7 \cdot i) (5 (i \cdot \sqrt{100}))$

Multiply $7$ by $- 2$ .

$- 14 i (5 (i \cdot \sqrt{100}))$

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

$- 14 i (5 (i \cdot \sqrt{10^{2}}))$

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

$- 14 i (5 (i \cdot 10))$

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

$- 14 i (5 (10 \cdot i))$

Multiply $10$ by $5$ .

$- 14 i (50 i)$

Multiply $- 14 i (50 i)$ .

Multiply $50$ by $- 14$ .

$- 700 i i$

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

$- 700 (i^{1} i)$

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

$- 700 (i^{1} i^{1})$

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

$- 700 i^{1 + 1}$

Add $1$ and $1$ .

$- 700 i^{2}$

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

$- 700 \cdot - 1$

Multiply $- 700$ by $- 1$ .

$700$