https://file.aiquickdraw.com/mathbot/file/17268421368351d4hkfvy.jpg

It seems that the text extraction from the image didn't work as expected. I will manually transcribe and solve the equation:

The expression is:

\[
\frac{-\frac{8}{9}x^3y^6}{\frac{9}{12}x^2y^2}
\]

Let's simplify step by step.

1. **Simplify the coefficients:**

\[
\frac{-\frac{8}{9}}{\frac{9}{12}} = -\frac{8}{9} \times \frac{12}{9} = -\frac{96}{81} = -\frac{32}{27}
\]

2. **Simplify the variables:**
   - For \(x\), we have \(x^3 / x^2 = x^{3-2} = x\)
   - For \(y\), we have \(y^6 / y^2 = y^{6-2} = y^4\)

Thus, the simplified expression becomes:

\[
-\frac{32}{27} x y^4
\]

Would you like more details on any step or further explanations?

Here are five related questions:
1. How do you simplify expressions with exponents when dividing powers of the same base?
2. Can you explain how to simplify fractions with coefficients?
3. How do negative coefficients affect the simplification process?
4. What are the general rules for dividing terms with variables?
5. How do you handle simplification when multiple variables are involved?

**Tip**: When simplifying fractions, always factor out and cancel common terms to make the process easier.

Simplify the expression (-8/9 * x^3 * y^6) / (9/12 * x^2 * y^2).

Learn how to simplify a rational expression involving both fractions and exponents: (-8/9 * x^3 * y^6) / (9/12 * x^2 * y^2). This example uses exponent rules and fraction simplification techniques. Suitable for students in Grades 9-12.

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