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

This expression involves simplifying powers of imaginary numbers and radicals. Here's a step-by-step solution:

**1. Simplifying the radicals:**

- $(\sqrt{3})^2 = 3$ (The square of a square root cancels out)

**2. Simplifying the imaginary powers:**

- (-8i)² = (-8)² * (i)² = 64 * (-1) = -64
- Remember that i² = -1

**3. Multiplying the results:**

- 3 * (-64) =
**-192**

Therefore, the simplified form of $(\sqrt{3})^2 \cdot (-8i)^2$ is **-192**.