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The given problem asks to change the exponential expression \( k^{\frac{5}{6}} \) into an equivalent radical expression. 

### Step-by-step solution:
1. The general rule for converting fractional exponents into radicals is:
   \[
   a^{\frac{m}{n}} = \sqrt[n]{a^m}
   \]
   where \( m \) is the exponent of the base \( a \), and \( n \) is the root.

2. Applying this rule to \( k^{\frac{5}{6}} \):
   - The base is \( k \).
   - The numerator \( 5 \) of the fraction becomes the exponent inside the radical.
   - The denominator \( 6 \) becomes the root of the radical.

Thus, \( k^{\frac{5}{6}} \) is equivalent to:
\[
\sqrt[6]{k^5}
\]

### Correct answer:
The answer is the fourth option: 
\[
\sqrt[6]{k^5}
\]

Would you like more details, or do you have any other questions? Here are 5 related questions to consider:

1. How do you simplify expressions with fractional exponents?
2. What is the relationship between exponents and roots?
3. How do you handle negative fractional exponents?
4. Can you convert a radical back to an exponential expression?
5. What are the different ways to express powers and roots?

**Tip:** When converting fractional exponents, always remember that the denominator of the exponent represents the root, and the numerator represents the power.

Change the exponential expression k^{5/6} to an equivalent radical expression.

Learn how to convert the exponential expression k^{5/6} into its equivalent radical form with a detailed step-by-step solution. This problem involves the rules for exponents and radicals, making it suitable for students in Grades 9-11.

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