The expression \((2x^2)^{\frac{1}{2}}\) can be simplified as follows:

1. First, apply the power of \(\frac{1}{2}\) (which is the square root) to the entire expression inside the parentheses:
   \[
   (2x^2)^{\frac{1}{2}} = \sqrt{2x^2}
   \]

2. Now, distribute the square root over the product inside:
   \[
   \sqrt{2x^2} = \sqrt{2} \cdot \sqrt{x^2}
   \]

3. Simplify \(\sqrt{x^2}\) to \(|x|\) because taking the square root of \(x^2\) results in the absolute value of \(x\):
   \[
   \sqrt{2} \cdot |x|
   \]

Thus, the simplified form of \((2x^2)^{\frac{1}{2}}\) is:
\[
\sqrt{2} \cdot |x|
\]

Would you like further clarification on any of these steps?

### Related Questions:
1. How would the expression change if the exponent were \(\frac{1}{3}\) instead of \(\frac{1}{2}\)?
2. What is the simplified form of \((3x^4)^{\frac{1}{2}}\)?
3. How does \((2x^2)^n\) change if \(n\) is a negative exponent?
4. Why do we take the absolute value of \(x\) when simplifying \(\sqrt{x^2}\)?
5. What if we have a cube root, such as \((2x^2)^{\frac{1}{3}}\)? How does it simplify?

### Tip:
When dealing with expressions like \((a \cdot b)^n\), remember that you can apply the exponent \(n\) to each term separately, as in \(a^n \cdot b^n\). This helps simplify complex expressions.

Explore how to simplify the expression (2x^2)^1/2 with a step-by-step breakdown. This guide covers square roots, exponents, and the absolute value property, making it suitable for students in Grades 9-10.

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