https://file.aiquickdraw.com/mathbot/file/1728260782659yvs38nle.jpg

Let's work through the problem shown in the image step by step.

### Problem:
You are asked to simplify and write the expression \((5a^{4/5})(4a^{4/5})\) in radical notation.

### Steps to Solve:

1. **Combine the constants**:
   \[
   5 \times 4 = 20
   \]
   So, the constants become \( 20 \).

2. **Combine the powers of \( a \)**:
   Both terms have \( a \) raised to the \( \frac{4}{5} \)-th power, so you add the exponents:
   \[
   a^{4/5} \times a^{4/5} = a^{(4/5 + 4/5)} = a^{8/5}
   \]

3. **Convert to radical notation**:
   The exponent \( a^{8/5} \) can be rewritten as:
   \[
   a^{8/5} = \sqrt[5]{a^8}
   \]
   Therefore, the expression becomes:
   \[
   20 \cdot \sqrt[5]{a^8}
   \]

### Answer:
From the choices given, the correct simplified form is:

\[
\boxed{C. \ 20 \sqrt[5]{a^8}}
\]

Would you like more details on any part of this? Feel free to ask!

### Follow-up Questions:
1. How would you simplify \((3a^{2/3})(7a^{1/3})\)?
2. What is the general rule for multiplying terms with the same base but different exponents?
3. How would you simplify \((6b^{1/2})(4b^{3/4})\)?
4. Can you explain why the expression \( a^{m/n} \) can be written in radical notation?
5. What happens if you subtract exponents when dividing terms with the same base?

### Tip:
When combining exponents with the same base, always remember to **add the exponents** for multiplication and **subtract them** for division.

Simplify and write in radical notation: (5a^4/5)(4a^4/5)

Learn how to simplify the expression (5a^4/5)(4a^4/5) step by step. This algebra problem involves exponent rules and radical notation, perfect for students in Grades 9-11.

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