To simplify the expression:

\[
\sqrt[4]{a^2} \cdot \sqrt[4]{a^2}
\]

1. **Apply the Property of Radicals:**
   The product of two fourth roots can be combined as a single fourth root:

   \[
   \sqrt[4]{a^2} \cdot \sqrt[4]{a^2} = \sqrt[4]{(a^2) \cdot (a^2)} = \sqrt[4]{a^4}
   \]

2. **Simplify the Result:**
   Since \( \sqrt[4]{a^4} = a \), the simplified form of the expression is:

   \[
   a
   \]

Therefore, the simplified expression is \( a \).

Would you like more details or have any questions?

Here are some related questions to consider:
1. How would the expression change if it were \( \sqrt[3]{a^2} \cdot \sqrt[3]{a^2} \)?
2. What happens if you multiply \( \sqrt[n]{a^m} \cdot \sqrt[n]{a^m} \) in general?
3. How does the simplification process differ for square roots versus

Learn how to simplify the expression \( \sqrt[4]{a^2} \cdot \sqrt[4]{a^2} \) step by step. This problem involves the application of radical and exponent properties and is suitable for students in Grades 9-11.

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