Simplify the Radical Expression (-12 square root of 12)(-3 square root of 3)

$(- 12 \sqrt{12}) (- 3 \sqrt{3})$

Rewrite $12$ as $2^{2} \cdot 3$ .

Factor $4$ out of $12$ .

$- 12 \sqrt{4 (3)} (- 3 \sqrt{3})$

Rewrite $4$ as $2^{2}$ .

$- 12 \sqrt{2^{2} \cdot 3} (- 3 \sqrt{3})$

Pull terms out from under the radical.

$- 12 (| 2 | \sqrt{3}) (- 3 \sqrt{3})$

The absolute value is the distance between a number and zero. The distance between $0$ and $2$ is $2$ .

$- 12 (2 \sqrt{3}) (- 3 \sqrt{3})$

Multiply $2$ by $- 12$ .

$- 24 \sqrt{3} (- 3 \sqrt{3})$

Multiply $- 24 \sqrt{3} (- 3 \sqrt{3})$ .

Multiply $- 3$ by $- 24$ .

$72 \sqrt{3} \sqrt{3}$

Raise $\sqrt{3}$ to the power of $1$ .

$72 ({\sqrt{3}}^{1} \sqrt{3})$

Raise $\sqrt{3}$ to the power of $1$ .

$72 ({\sqrt{3}}^{1} {\sqrt{3}}^{1})$

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

$72 {\sqrt{3}}^{1 + 1}$

Add $1$ and $1$ .

$72 {\sqrt{3}}^{2}$

Rewrite ${\sqrt{3}}^{2}$ as $3$ .

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{3}$ as $3^{\frac{1}{2}}$ .

$72 {(3^{\frac{1}{2}})}^{2}$

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$72 \cdot 3^{\frac{1}{2} \cdot 2}$

Combine $\frac{1}{2}$ and $2$ .

$72 \cdot 3^{\frac{2}{2}}$

Cancel the common factor of $2$ .

Cancel the common factor.

$72 \cdot 3^{\frac{2}{2}}$

Rewrite the expression.

$72 \cdot 3^{1}$

Evaluate the exponent.

$72 \cdot 3$

Multiply $72$ by $3$ .

$216$