Simplify 2x^3 square root of -27x^3

$2 x^{3} \sqrt{- 27 x^{3}}$

Rewrite $- 27 x^{3}$ as ${(3 x)}^{2} \cdot (- 3 x)$ .

Factor $9$ out of $- 27$ .

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

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

$2 x^{3} \sqrt{3^{2} \cdot - 3 x^{3}}$

Factor out $x^{2}$ .

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

Move $- 3$ .

$2 x^{3} \sqrt{3^{2} x^{2} \cdot - 3 x}$

Rewrite $3^{2} x^{2}$ as ${(3 x)}^{2}$ .

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

Add parentheses.

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

Pull terms out from under the radical.

$2 x^{3} (3 x \sqrt{- 3 x})$

Multiply $x^{3}$ by $x$ by adding the exponents.

Move $x$ .

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

Multiply $x$ by $x^{3}$ .

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

$2 (x^{1} x^{3}) (3 \sqrt{- 3 x})$

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

$2 x^{1 + 3} (3 \sqrt{- 3 x})$

Add $1$ and $3$ .

$2 x^{4} (3 \sqrt{- 3 x})$

Multiply $3$ by $2$ .

$6 x^{4} \sqrt{- 3 x}$