https://file.aiquickdraw.com/mathbot/file/1729371467683rhtr6o2h.jpg

Let's analyze the options to determine which expression is a perfect square.

1. **Option 1: \( 256z^4 \)**  
   - \( 256 \) is a perfect square because \( 256 = 16^2 \).
   - \( z^4 \) is also a perfect square because \( z^4 = (z^2)^2 \).
   - Therefore, \( 256z^4 \) is a perfect square.

2. **Option 2: \( 25x \)**  
   - \( 25 \) is a perfect square because \( 25 = 5^2 \), but \( x \) alone is not necessarily a perfect square unless more information about \( x \) is given. Therefore, \( 25x \) is not guaranteed to be a perfect square.

3. **Option 3: \( 66 \)**  
   - \( 66 \) is not a perfect square because no integer squared gives 66.

4. **Option 4: \( 110 \)**  
   - \( 110 \) is not a perfect square for the same reason as 66; no integer squared gives 110.

### Conclusion:
The correct answer is **\( 256z^4 \)**, which is a perfect square.

Would you like more details or have any questions about this solution?  
Here are five related questions:

1. How do you determine if a number is a perfect square?
2. Can a variable expression, like \( z^4 \), always be considered a perfect square?
3. Why is \( 256 \) a perfect square but \( 66 \) is not?
4. How can we generalize the process of finding perfect squares in algebraic expressions?
5. What role do exponents play in determining whether an expression is a perfect square?

**Tip:** A number is a perfect square if its prime factors all have even exponents.

Which is a perfect square? Options: 256z^4, 25x, 66, 110.

Determine which expression is a perfect square from the options 256z^4, 25x, 66, and 110. This problem covers the concepts of perfect squares and exponent rules. Suitable for students in Grades 8-10.

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