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To simplify the given expression \(\frac{k^{\frac{2}{3}}}{k^{\frac{5}{12}}}\), we will use the property of exponents:

\[
\frac{a^m}{a^n} = a^{m - n}
\]

### Step-by-Step Solution
1. Rewrite the expression by applying the exponent rule:
   \[
   \frac{k^{\frac{2}{3}}}{k^{\frac{5}{12}}} = k^{\frac{2}{3} - \frac{5}{12}}
   \]

2. Find a common denominator for \(\frac{2}{3}\) and \(\frac{5}{12}\):
   - The least common multiple of 3 and 12 is 12.
   - Convert \(\frac{2}{3}\) to \(\frac{8}{12}\):
     \[
     \frac{2}{3} = \frac{8}{12}
     \]

3. Subtract the exponents:
   \[
   k^{\frac{8}{12} - \frac{5}{12}} = k^{\frac{3}{12}} = k^{\frac{1}{4}}
   \]

4. Rewrite \(k^{\frac{1}{4}}\) in radical form:
   \[
   k^{\frac{1}{4}} = \sqrt[4]{k}
   \]

### Answer
The expression in simplest radical form is:
\[
\sqrt[4]{k}
\]

### Correct Answer Choice
The correct choice is:
\[
\sqrt[4]{k}
\]

Would you like further details on any part of this solution, or have any additional questions?

### Related Questions
1. How do you simplify expressions with different bases?
2. What is the general rule for subtracting exponents?
3. How can you convert fractional exponents to radical form?
4. Why do we use the least common multiple when subtracting fractions?
5. How can we simplify complex expressions involving roots and exponents?

### Tip
When simplifying expressions with exponents, always try to rewrite fractions with a common denominator to make addition or subtraction easier.

Simplify. Write the expression in simplest radical form: \( \frac{k^{\frac{2}{3}}}{k^{\frac{5}{12}}} \)

Learn how to simplify \( \frac{k^{\frac{2}{3}}}{k^{\frac{5}{12}}} \) and express it in simplest radical form. This problem involves using properties of exponents, including exponent subtraction and conversion to radical notation. Suitable for high school students in Grades 9-12.

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