The expression in the image is:

$\frac{x^{-4} y^2}{x^{-6} y^5}$

Let's simplify this step by step.

Step 1: Simplify the powers of $x$

Using the rule of exponents $\frac{a^m}{a^n} = a^{m-n}$, we can simplify the $x$-terms:

$\frac{x^{-4}}{x^{-6}} = x^{-4 - (-6)} = x^{-4 + 6} = x^2$

Step 2: Simplify the powers of $y$

Similarly, for the $y$-terms:

$\frac{y^2}{y^5} = y^{2 - 5} = y^{-3}$

Step 3: Combine the results

After simplifying both the $x$- and $y$-terms, the expression becomes:

$x^2 y^{-3}$

This is the simplified form of the given expression. Alternatively, we can write the $y^{-3}$ term as a fraction:

$\frac{x^2}{y^3}$

Would you like more details on any of the steps, or have any other questions?

Here are five related questions you might find useful:

1. How do you simplify expressions with more complex exponents?
2. What are the rules for negative exponents?
3. How would you simplify an expression with three variables, such as $x^{-3}y^4z^{-2}$?
4. How do fractional exponents work in simplification?
5. What is the process for simplifying radical expressions?

Tip: When working with exponents, always remember the basic exponent rules: $a^m \times a^n = a^{m+n}$ and $\frac{a^m}{a^n} = a^{m-n}$.