The expression in the image appears to be the limit of the following function as $x$ approaches 5:

$\lim_{{x \to 5}} \sqrt[4] {\frac{3x + 1}{3x - 1}}$

Let's evaluate this limit step by step:

1. Substitute $x = 5$ into the function: $\frac{3(5) + 1}{3(5) - 1} = \frac{15 + 1}{15 - 1} = \frac{16}{14} = \frac{8}{7}$

2. Now take the fourth root: $\sqrt[4]{\frac{8}{7}}$

This is the simplified limit expression. The exact result is $\sqrt[4]{\frac{8}{7}}$.

Would you like to explore this in more detail, or have any other questions?

Here are five related questions to deepen your understanding:

1. What is the difference between evaluating a limit and finding a derivative?
2. How do you handle limits that result in indeterminate forms (e.g., $\frac{0}{0}$)?
3. What is the significance of higher-order roots, like the fourth root, in calculus?
4. How can L'Hopital's Rule be applied to limit problems?
5. What is the general form of a continuous function, and why is continuity important in limits?

Tip: When evaluating limits, substituting the value directly into the function is the first step. If it leads to indeterminate forms, other techniques like factoring or L'Hopital's Rule might be necessary!