Simplify (-2 square root of 7)(3 square root of 28)

$(- 2 \sqrt{7}) (3 \sqrt{28})$

Rewrite $28$ as $2^{2} \cdot 7$ .

Factor $4$ out of $28$ .

$- 2 \sqrt{7} (3 \sqrt{4 (7)})$

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

$- 2 \sqrt{7} (3 \sqrt{2^{2} \cdot 7})$

Pull terms out from under the radical.

$- 2 \sqrt{7} (3 (2 \sqrt{7}))$

Multiply $2$ by $3$ .

$- 2 \sqrt{7} (6 \sqrt{7})$

Multiply $- 2 \sqrt{7} (6 \sqrt{7})$ .

Multiply $6$ by $- 2$ .

$- 12 \sqrt{7} \sqrt{7}$

Raise $\sqrt{7}$ to the power of $1$ .

$- 12 ({\sqrt{7}}^{1} \sqrt{7})$

Raise $\sqrt{7}$ to the power of $1$ .

$- 12 ({\sqrt{7}}^{1} {\sqrt{7}}^{1})$

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

$- 12 {\sqrt{7}}^{1 + 1}$

Add $1$ and $1$ .

$- 12 {\sqrt{7}}^{2}$

Rewrite ${\sqrt{7}}^{2}$ as $7$ .

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{7}$ as $7^{\frac{1}{2}}$ .

$- 12 {(7^{\frac{1}{2}})}^{2}$

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

$- 12 \cdot 7^{\frac{1}{2} \cdot 2}$

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

$- 12 \cdot 7^{\frac{2}{2}}$

Cancel the common factor of $2$ .

Cancel the common factor.

$- 12 \cdot 7^{\frac{2}{2}}$

Rewrite the expression.

$- 12 \cdot 7^{1}$

Evaluate the exponent.

$- 12 \cdot 7$

Multiply $- 12$ by $7$ .

$- 84$