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The given expression is:

\[
\sqrt[5]{(9a)^2}
\]

To express this in **exponential form**, let's break it down:

### Step 1: Rewriting the Root
The fifth root, \(\sqrt[5]{x}\), can be rewritten as \(x^{1/5}\).

So, \(\sqrt[5]{(9a)^2}\) becomes:
\[
(9a)^2 = (9a)^{2/5}
\]

### Step 2: Applying Exponent Rules
Now distribute the exponent \(2/5\) to both \(9\) and \(a\). This gives:
\[
9^{2/5} \cdot a^{2/5}
\]

### Final Exponential Form:
Thus, the expression in exponential form is:
\[
9^{2/5} \cdot a^{2/5}
\]

---

Would you like further clarification or details on any part of the process?

Here are 5 related questions you might find useful:

1. How do you simplify expressions involving fractional exponents?
2. How do you handle cube roots and other roots in exponential form?
3. What is the difference between radical notation and exponential notation?
4. Can all radicals be written in terms of fractional exponents?
5. How can you apply exponent rules to simplify expressions further?

**Tip**: When converting a radical to exponential form, always remember that \( \sqrt[n]{x} = x^{1/n} \).

Write the expression below in exponential form: \( \sqrt[5]{(9a)^2} \)

Learn how to express \( \sqrt[5]{(9a)^2} \) in exponential form using fractional exponents. This guide breaks down the step-by-step conversion of radicals to exponents and applies exponent rules. Suitable for Grades 9-12 students.

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