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.