Simplify -2 square root of 64+5 square root of -64+ cube root of -729

$- 2 \sqrt{64} + 5 \sqrt{- 64} + \sqrt[3]{- 729}$

Simplify each term.

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

$- 2 \sqrt{8^{2}} + 5 \sqrt{- 64} + \sqrt[3]{- 729}$

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

$- 2 \cdot 8 + 5 \sqrt{- 64} + \sqrt[3]{- 729}$

Multiply $- 2$ by $8$ .

$- 16 + 5 \sqrt{- 64} + \sqrt[3]{- 729}$

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

$- 16 + 5 \sqrt{- 1 (64)} + \sqrt[3]{- 729}$

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

$- 16 + 5 (\sqrt{- 1} \cdot \sqrt{64}) + \sqrt[3]{- 729}$

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

$- 16 + 5 (i \cdot \sqrt{64}) + \sqrt[3]{- 729}$

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

$- 16 + 5 (i \cdot \sqrt{8^{2}}) + \sqrt[3]{- 729}$

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

$- 16 + 5 (i \cdot 8) + \sqrt[3]{- 729}$

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

$- 16 + 5 (8 \cdot i) + \sqrt[3]{- 729}$

Multiply $8$ by $5$ .

$- 16 + 40 i + \sqrt[3]{- 729}$

Rewrite $- 729$ as ${(- 9)}^{3}$ .

$- 16 + 40 i + \sqrt[3]{{(- 9)}^{3}}$

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

$- 16 + 40 i - 9$

Subtract $9$ from $- 16$ .

$- 25 + 40 i$