1) \( \sqrt{n^{8}} \)

The expression \( \sqrt{n^{8}} \) simplifies beautifully! When you take the square root of a power, you essentially divide the exponent by 2. Thus, \( \sqrt{n^{8}} = n^{4} \). So, for any value of \( n \), this is your clean and crisp result, showcasing the power of exponents! In real-world applications, such square root simplifications often pop up in fields like engineering and physics where calculations involving formulas can get quite complex. For instance, if you're calculating the area of a square related to stress distribution, simplifying powers like \( n^8 \) to \( n^4 \) helps in making the math more manageable and keeps those equations neat!