Simplify (-3 square root of 27)( square root of -81)

$(- 3 \sqrt{27}) (\sqrt{- 81})$

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

$- 3 \sqrt{27} \sqrt{- 1 (81)}$

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

$- 3 \sqrt{27} (\sqrt{- 1} \cdot \sqrt{81})$

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

$- 3 \sqrt{27} (i \cdot \sqrt{81})$

Rewrite $27$ as $3^{2} \cdot 3$ .

Factor $9$ out of $27$ .

$- 3 \sqrt{9 (3)} (i \cdot \sqrt{81})$

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

$- 3 \sqrt{3^{2} \cdot 3} (i \cdot \sqrt{81})$

Pull terms out from under the radical.

$- 3 (3 \sqrt{3}) (i \cdot \sqrt{81})$

Simplify the expression.

Multiply $3$ by $- 3$ .

$- 9 \sqrt{3} (i \cdot \sqrt{81})$

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

$- 9 \sqrt{3} (i \cdot \sqrt{9^{2}})$

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

$- 9 \sqrt{3} (i \cdot 9)$

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

$- 9 \sqrt{3} (9 \cdot i)$

Multiply $9$ by $- 9$ .

$- 81 \sqrt{3} i$