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?

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.