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To simplify the expression \(\sqrt{x^8}\), we need to understand that a square root of a power can be simplified by dividing the exponent by 2.

Here's the step-by-step solution:

1. The expression is \(\sqrt{x^8}\).
2. We can rewrite this as \(x^{8/2}\).
3. Simplifying the exponent, we get \(x^4\).

Thus, \(\sqrt{x^8} = x^4\).

The simplified answer is:
\[
x^4
\]

Would you like a more detailed explanation, or do you have any questions?

### Related Questions:
1. How would you simplify \(\sqrt{x^{10}}\)?
2. What is the simplification of \(\sqrt{y^{12}}\) assuming \(y\) is nonnegative?
3. How do you simplify \(\sqrt{x^{16}}\)?
4. What happens if the exponent is odd, such as in \(\sqrt{x^7}\)?
5. How would you express \(\sqrt{x^{8}} \cdot \sqrt{x^{6}}\) in simplest form?

### Tip:
For any square root \(\sqrt{x^n}\), you can simplify it by dividing \(n\) by 2, provided \(n\) is even.

Simplify \(\sqrt{x^8}\), assuming variables represent nonnegative values.

Learn how to simplify \(\sqrt{x^8}\) by using exponent rules. This problem covers algebraic concepts related to roots and exponentiation, perfect for students in Grades 7-8.

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