The expression you're being asked to simplify is:

$\left( \sqrt{-16} \right) \left( \sqrt{-25} \right)$

Here’s how to approach it:

1. Simplify each square root:

   • $\sqrt{-16} = \sqrt{16} \cdot \sqrt{-1} = 4i$ (where $i$ is the imaginary unit, because $\sqrt{-1} = i$).
   • $\sqrt{-25} = \sqrt{25} \cdot \sqrt{-1} = 5i$.

2. Multiply the simplified results: $(4i) \cdot (5i) = 20i^2$

3. Simplify further using the fact that $i^2 = -1$: $20i^2 = 20 \cdot (-1) = -20$

So, the simplified answer is -20.

Would you like more details, or do you have any questions about this solution?

Here are 5 related questions to deepen understanding:

1. What is the general rule for simplifying square roots of negative numbers?
2. Why is $i^2$ defined as $-1$ in complex numbers?
3. How would you multiply other complex numbers like $(3 + 2i)$ and $(4 - i)$?
4. What happens if you have square roots with mixed real and imaginary components, like $\sqrt{16} \cdot \sqrt{-25}$?
5. How do you graph complex numbers on the complex plane?

Tip: Always handle imaginary numbers carefully, making sure to simplify $i^2$ when multiplying them!