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To simplify the expression \( \left( \frac{4x}{yz} \right)^2 \), we proceed as follows:

1. **Square the numerator and the denominator:**
   \[
   \left( \frac{4x}{yz} \right)^2 = \frac{(4x)^2}{(yz)^2}
   \]

2. **Calculate each squared term:**
   - For the numerator: \((4x)^2 = 16x^2\)
   - For the denominator: \((yz)^2 = y^2z^2\)

3. **Combine the results:**
   \[
   \frac{16x^2}{y^2z^2}
   \]

So, the fully simplified expression is:
\[
\frac{16x^2}{y^2z^2}
\]

### Answer:
The correct answer is the second option: \( \frac{16x^2}{y^2z^2} \).

Would you like further details, or do you have any questions?

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Here are some related questions to practice:

1. How would you simplify \( \left( \frac{3a}{b} \right)^3 \)?
2. What is the result of \( \left( \frac{2x^2}{3y} \right)^2 \)?
3. If you have \( \left( \frac{x}{y} \right)^n \), how does the exponent affect each part?
4. How would you handle \( \left( \frac{5xy}{2z} \right)^2 \)?
5. What is the simplified form of \( \frac{(4x^2y)^2}{(2z)^2} \)?

### Tip:
Remember, when squaring a fraction, square both the numerator and the denominator separately before combining them.

Completely simplify the expression (4x / yz)^2.

Learn how to simplify the algebraic expression (4x / yz)^2 by applying exponent rules. This step-by-step solution covers squaring both the numerator and denominator, resulting in the simplified form 16x^2 / y^2z^2. Ideal for students in Grades 9-10.

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