https://file.aiquickdraw.com/mathbot/file/17254678133057kgmbko6.jpg

To solve this problem, we need to find which of the given options is equivalent to the expression \( x^{\frac{5}{8}} \).

### Step-by-Step Solution:

1. **Understanding the Expression:**
   - The expression \( x^{\frac{5}{8}} \) can be rewritten using the properties of exponents and radicals. Specifically, \( x^{\frac{m}{n}} = \sqrt[n]{x^m} \).

2. **Rewriting \( x^{\frac{5}{8}} \):**
   - \( x^{\frac{5}{8}} \) can be rewritten as \( \sqrt[8]{x^5} \).

3. **Compare with the Options:**
   - **Option A:** \( \sqrt[8]{x^5} \) → This matches exactly with our expression.
   - **Option B:** \( \sqrt[5]{x^8} \) → This is equivalent to \( x^{\frac{8}{5}} \), not \( x^{\frac{5}{8}} \).
   - **Option C:** \( \sqrt[8]{x^5} \) → This is exactly the same as Option A, and therefore also correct.

### Conclusion:
The correct answer is **Option A** (which is the same as Option C), \( \sqrt[8]{x^5} \).

Would you like further details or have any other questions?

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### Related Questions:
1. What is the general rule for converting fractional exponents to radical expressions?
2. How do you simplify an expression like \( x^{\frac{3}{4}} \)?
3. What is the difference between \( \sqrt[n]{x^m} \) and \( x^{\frac{m}{n}} \)?
4. How can you express \( \sqrt[3]{x^2} \) as a power of \( x \)?
5. What does \( x^{\frac{n}{m}} \) represent in terms of radical notation?

### Tip:
Remember, the denominator in a fractional exponent represents the root, while the numerator represents the power.

Which of the following is equivalent to x^(5/8)?

Learn how to convert the fractional exponent x^(5/8) into a radical expression with this step-by-step solution. This guide covers key concepts in exponents and radicals, suitable for high school students.

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