Simplify (i square root of 3)^2*(-8i)^2

${(i \sqrt{3})}^{2} \cdot {(- 8 i)}^{2}$

Apply the product rule to $i \sqrt{3}$ .

$i^{2} {\sqrt{3}}^{2} \cdot {(- 8 i)}^{2}$

Rewrite $i^{2}$ as $- 1$ .

$- 1 {\sqrt{3}}^{2} \cdot {(- 8 i)}^{2}$

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

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

$- 1 {(3^{\frac{1}{2}})}^{2} \cdot {(- 8 i)}^{2}$

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

$- 1 \cdot 3^{\frac{1}{2} \cdot 2} \cdot {(- 8 i)}^{2}$

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

$- 1 \cdot 3^{\frac{2}{2}} \cdot {(- 8 i)}^{2}$

Cancel the common factor of $2$ .

Cancel the common factor.

$- 1 \cdot 3^{\frac{2}{2}} \cdot {(- 8 i)}^{2}$

Rewrite the expression.

$- 1 \cdot 3^{1} \cdot {(- 8 i)}^{2}$

Evaluate the exponent.

$- 1 \cdot 3 \cdot {(- 8 i)}^{2}$

Simplify the expression.

Multiply $- 1$ by $3$ .

$- 3 \cdot {(- 8 i)}^{2}$

Apply the product rule to $- 8 i$ .

$- 3 \cdot ({(- 8)}^{2} i^{2})$

Raise $- 8$ to the power of $2$ .

$- 3 \cdot (64 i^{2})$

Rewrite $i^{2}$ as $- 1$ .

$- 3 \cdot (64 \cdot - 1)$

Multiply $64$ by $- 1$ .

$- 3 \cdot - 64$

Multiply $- 3$ by $- 64$ .

$192$