We are tasked with simplifying the expression:

\[
\frac{-25x^{11}y^7}{5x^3y^4}
\]

### Step 1: Simplify the coefficients
The coefficients are \(-25\) and \(5\). Divide:
\[
\frac{-25}{5} = -5
\]

### Step 2: Simplify the powers of \(x\)
For the powers of \(x\), use the property of exponents: 
\[
\frac{x^{11}}{x^3} = x^{11 - 3} = x^8
\]

### Step 3: Simplify the powers of \(y\)
Similarly, simplify the powers of \(y\):
\[
\frac{y^7}{y^4} = y^{7 - 4} = y^3
\]

### Final Expression
After simplifying, the expression becomes:
\[
-5x^8y^3
\]

Would you like more details or further explanations?

### Related Questions:
1. How do you simplify expressions with negative exponents?
2. What is the rule for dividing terms with the same base in exponents?
3. How would the process change with different variables?
4. Can you apply these rules to fractional exponents?
5. How do you simplify expressions with multiple variables?

### Tip:
When dividing terms with the same base, subtract the exponents!

This guide explains how to simplify the expression 25x^11y^7 / 5x^3y^4 step by step. Learn how to apply exponent rules and algebraic simplification techniques. Suitable for students in Grades 9-10.

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