(akar pangkat 3 dari 7^2) / (akar pangkat 7 dari 7^6) =

We need to simplify the expression \(\frac{\sqrt[3]{7^2}}{\sqrt[7]{7^6}}\).

### Steps to Simplify:

1. **Rewrite the radicals as exponents:**

   Recall that \(\sqrt[n]{a^m}\) can be rewritten as \(a^{\frac{m}{n}}\). So, we rewrite the expression:
   \[
   \frac{\sqrt[3]{7^2}}{\sqrt[7]{7^6}} = \frac{7^{\frac{2}{3}}}{7^{\frac{6}{7}}}
   \]

2. **Simplify the expression:**

   Using the property of exponents \(\frac{a^m}{a^n} = a^{m-n}\), we can simplify the expression:
   \[
   7^{\frac{2}{3} - \frac{6}{7}}
   \]

3. **Find a common denominator:**

   To subtract the exponents \(\frac{2}{3}\) and \(\frac{6}{7}\), we need to find a common denominator:
   \[
   \frac{2}{3} = \frac{14}{21}, \quad \frac{6}{7} = \frac{18}{21}
   \]
   So, subtracting the exponents:
   \[
   \frac{2}{3} - \frac{6}{7} = \frac{14}{21} - \frac{18}{21} = \frac{-4}{21}
   \]

4. **Final expression:**

   Thus, the expression simplifies to:
   \[
   7^{-\frac{4}{21}}
   \]

5. **Rewrite with a positive exponent (if necessary):**

   The final answer can be left as \(7^{-\frac{4}{21}}\) or written as a positive exponent:
   \[
   \frac{1}{7^{\frac{4}{21}}}
   \]

### Final Answer:
The simplified form of \(\frac{\sqrt[3]{7^2}}{\sqrt[7]{7^6}}\) is:
\[
\boxed{7^{-\frac{4}{21}}} \quad \text{or} \quad \boxed{\frac{1}{7^{\frac{4}{21}}}}
\]

Do you need further clarification or have any questions about this solution?

### Related Questions:
1. How do you simplify expressions with multiple radicals and different bases?
2. Can you explain the exponent rules when dealing with fractional exponents?
3. What is the importance of finding a common denominator when subtracting fractions?
4. How can simplifying such expressions be applied in real-world scenarios?
5. Can you show an example where simplifying complex exponents is useful in solving equations?

### Tip:
When dealing with fractional exponents, always try to express the problem in terms of the same base and simplify using exponent rules. This makes the calculation much easier.

Learn how to simplify the radical expression (cube root of 7^2) divided by (7th root of 7^6) step-by-step. This problem involves radicals, exponents, and fractional exponents, suitable for high school students.

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