The expression shown in the image is:

$\frac{2x^9 y^8}{x y^3} \div (4x^2 y^4)$

To solve this, let's follow the steps.

Step 1: Simplify the Fraction

Start by simplifying the fraction $\frac{2x^9 y^8}{x y^3}$:

1. Simplify the $x$-terms: $x^9 \div x = x^{9 - 1} = x^8$.
2. Simplify the $y$-terms: $y^8 \div y^3 = y^{8 - 3} = y^5$.

So, $\frac{2x^9 y^8}{x y^3} = 2x^8 y^5$.

Step 2: Set Up the Division

Now we need to divide $2x^8 y^5$ by $4x^2 y^4$:

$\frac{2x^8 y^5}{4x^2 y^4}$

Step 3: Simplify the Division

1. Simplify the constants: $\frac{2}{4} = \frac{1}{2}$.
2. Simplify the $x$-terms: $x^8 \div x^2 = x^{8 - 2} = x^6$.
3. Simplify the $y$-terms: $y^5 \div y^4 = y^{5 - 4} = y^1 = y$.

Combining these, we get:

$\frac{2x^8 y^5}{4x^2 y^4} = \frac{1}{2} x^6 y$

Final Answer

The simplified result is:

$\frac{1}{2} x^6 y$

Would you like more details or have any questions about the steps?

Here are some related questions:

1. How do you simplify expressions with exponents?
2. What are the rules for dividing terms with the same base?
3. How do coefficients affect division in algebraic expressions?
4. Why is simplifying terms with the same base important in algebra?
5. How does dividing by a fraction differ from dividing by a whole number?

Tip: Always handle constants and variables separately in expressions to avoid confusion in simplification steps.