Simplify (4 square root of 81)(4 square root of -64)

$(4 \sqrt{81}) (4 \sqrt{- 64})$

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

$4 \sqrt{81} (4 \sqrt{- 1 (64)})$

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

$4 \sqrt{81} (4 (\sqrt{- 1} \cdot \sqrt{64}))$

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

$4 \sqrt{81} (4 (i \cdot \sqrt{64}))$

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

$4 \sqrt{9^{2}} (4 (i \cdot \sqrt{64}))$

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

$4 \cdot 9 (4 (i \cdot \sqrt{64}))$

Multiply $4$ by $9$ .

$36 (4 (i \cdot \sqrt{64}))$

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

$36 (4 (i \cdot \sqrt{8^{2}}))$

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

$36 (4 (i \cdot 8))$

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

$36 (4 (8 \cdot i))$

Multiply $8$ by $4$ .

$36 (32 i)$

Multiply $32$ by $36$ .

$1152 i$