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The image you've uploaded contains a math problem with multiple-choice answers. I'll read and analyze the content to help you solve it.

**Problem Statement:**

It seems to be a question related to simplifying a mathematical expression:

The options provided are:
- \[ a. \sqrt{16x^2} \]
- \[ b. 2\sqrt{4x} \]
- \[ c. 4|x| \]
- \[ d. 4x^2 \]

Given the context, the problem likely asks for the simplification of the square root of a squared term. The correct answer should be the absolute value of the term within the square root, as \(\sqrt{(a)^2} = |a|\). Therefore, the simplified form is likely \(\sqrt{16x^2} = 4|x|\), matching option **c.** 4|x|.

Would you like a detailed explanation or have any further questions?

### Related Questions:
1. How do you simplify expressions under a square root?
2. Why do we use the absolute value when simplifying \(\sqrt{(a)^2}\)?
3. What are the properties of square roots and exponents?
4. How do different algebraic operations affect the outcome of simplifications?
5. Can you provide more examples of simplifying similar square root expressions?

**Tip:** Always remember that when simplifying square roots of squared variables, the result should account for both positive and negative values by using absolute values where appropriate.

Learn how to simplify the square root of 16x^2 with a detailed explanation. This problem involves understanding square roots and absolute values, crucial for high school mathematics. Find step-by-step solutions and related concepts.

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