To determine which expressions simplify to have a value of 16, let’s analyze each option:

1. $2\sqrt{64}$:

   • Simplify $\sqrt{64}$: $\sqrt{64} = 8$.
   • Multiply by 2: $2 \times 8 = 16$.
     This expression simplifies to 16.

2. $8^2$:

   • Simplify $8^2$: $8 \times 8 = 64$.
     This does not simplify to 16.

3. $2\sqrt{8}$:

   • Simplify $\sqrt{8}$: $\sqrt{8} = 2\sqrt{2}$.
   • Multiply by 2: $2 \times 2\sqrt{2} = 4\sqrt{2}$.
     This does not simplify to 16.

4. $2^4$:

   • Simplify $2^4$: $2 \times 2 \times 2 \times 2 = 16$.
     This expression simplifies to 16.

Correct answers:

• $2\sqrt{64}$
• $2^4$

Let me know if you'd like further clarification!

Expanding Questions:

1. What is the relationship between exponents and square roots in simplification?
2. How can radical expressions like $2\sqrt{8}$ be rewritten in simplest terms?
3. Why is $8^2$ not equal to 16 but much larger?
4. How do operations like squaring and multiplying differ when simplifying?
5. Can $2\sqrt{64}$ be rewritten as a power expression?

Tip: Always simplify square roots and perform operations step by step to avoid mistakes.