https://file.aiquickdraw.com/mathbot/file/1725590294065klcwjivk.jpg

The expression in the image is:

\[
\frac{w^{\frac{6}{5}} \cdot w^{\frac{4}{5}}}{w^{\frac{1}{5}}}
\]

We can simplify this using the properties of exponents.

### Step-by-step simplification:

1. **Multiply powers with the same base**:
   When multiplying powers with the same base, we add the exponents:
   \[
   w^{\frac{6}{5}} \cdot w^{\frac{4}{5}} = w^{\frac{6}{5} + \frac{4}{5}} = w^{\frac{10}{5}} = w^2
   \]

2. **Simplify the division of powers**:
   When dividing powers with the same base, we subtract the exponents:
   \[
   \frac{w^2}{w^{\frac{1}{5}}} = w^{2 - \frac{1}{5}} = w^{\frac{10}{5} - \frac{1}{5}} = w^{\frac{9}{5}}
   \]

Thus, the simplified expression is:

\[
w^{\frac{9}{5}}
\]

Would you like more details or have any questions?

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Here are 5 related questions to explore further:
1. What are the laws of exponents and how do they work in more complex cases?
2. How do you handle negative exponents in a similar expression?
3. How would this expression change if it had a different base, such as \(x\) instead of \(w\)?
4. What happens when fractional exponents involve roots, like \( w^{\frac{1}{2}} \)?
5. How would you simplify an expression involving addition or subtraction of powers instead of multiplication?

**Tip**: When working with exponents, always remember to combine them by adding when multiplying and subtracting when dividing.

Simplify the expression (w^(6/5) * w^(4/5)) / w^(1/5).

Learn how to simplify the exponential expression (w^(6/5) * w^(4/5)) / w^(1/5) using the laws of exponents. This step-by-step guide explains how to add and subtract exponents for expressions with the same base. Suitable for students in Grades 8-10.

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