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!