https://file.aiquickdraw.com/mathbot/file/1726568786594jkg55kxi.jpg

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?

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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 \( \frac{a^m}{a^n} = a^{m-n} \).

Simplify the expression (x^-4 * y^2) / (x^-6 * y^5).

Learn how to simplify the algebraic expression (x^-4 * y^2) / (x^-6 * y^5) by applying the exponent rules. This detailed solution covers concepts like the rule of exponents and negative exponents. Suitable for students in Grades 8-10.

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