Let's solve the given problem:

The expression to simplify is:

$\sqrt{16y^{16}}$

Step-by-Step Solution:

1. Split the square root: $\sqrt{16y^{16}} = \sqrt{16} \cdot \sqrt{y^{16}}$

2. Simplify each part:

   • $\sqrt{16} = 4$
   • $\sqrt{y^{16}} = y^{16/2} = y^8$

3. Combine the results: $\sqrt{16y^{16}} = 4y^8$

Final Answer:

The simplified form is: $4y^8$

The correct choice is: $4y^8$.

Would you like additional clarification or related practice problems? Here are some questions to explore further:

1. How do you simplify $\sqrt{49x^{14}}$?
2. Can you explain the rule for simplifying $\sqrt{x^n}$?
3. What is the simplified form of $\sqrt{36z^{20}}$?
4. What happens if the exponent in $y^{16}$ is odd? How would the result change?
5. Why is $\sqrt{a^2} = |a|$ in general?

Tip: When simplifying square roots, always check for even powers to simplify exponents efficiently!