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The image you uploaded contains a mathematical expression under a radical with several answer options. The question appears to be simplifying an expression. I can make out part of the problem as follows:

\[
\sqrt[6]{\sqrt[5]{\sqrt[4]{x^{14}}}} = ?
\]

The answer choices include:

- (A) \( x^{\frac{2}{5}} \)
- (B) \( x^{\frac{2}{3}} \)
- (C) \( x^{\frac{5}{12}} \)
- (D) \( x^{\frac{2}{7}} \)
- (E) \( x^{\frac{1}{2}} \)

### Solution:
We need to simplify the expression step by step:

1. Start with the innermost radical:
   \[
   \sqrt[4]{x^{14}} = x^{\frac{14}{4}} = x^{\frac{7}{2}}
   \]

2. Apply the next radical:
   \[
   \sqrt[5]{x^{\frac{7}{2}}} = x^{\frac{7}{2} \cdot \frac{1}{5}} = x^{\frac{7}{10}}
   \]

3. Finally, apply the outermost radical:
   \[
   \sqrt[6]{x^{\frac{7}{10}}} = x^{\frac{7}{10} \cdot \frac{1}{6}} = x^{\frac{7}{60}}
   \]

Thus, the simplified expression is:
\[
x^{\frac{7}{60}}
\]

However, none of the provided answer choices directly match \(x^{\frac{7}{60}}\). There may be a printing or transcription issue with the answer options.

Would you like more details on this? Here are some related questions to expand on this topic:

1. How do you handle more complex nested radicals in different variables?
2. What are the rules for simplifying expressions involving fractional exponents?
3. Can you explain the difference between simplifying radicals and exponential expressions?
4. What is the general form for expressing a radical as an exponent?
5. How do we apply the chain rule for radicals in calculus?

**Tip:** Always break down radicals from the innermost expression outward when simplifying nested radicals.

Simplify the expression: \sqrt[6]{\sqrt[5]{\sqrt[4]{x^{14}}}} and choose the correct answer.

This problem involves simplifying the nested radical expression \sqrt[6]{\sqrt[5]{\sqrt[4]{x^{14}}}}. Learn step-by-step how to simplify radicals and apply the laws of exponents, suitable for Grades 9-12.

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