To simplify the expression:

\[
\frac{-4x^8y^{10}}{2x^7y^{10}}
\]

We can follow these steps:

1. **Simplify the coefficients**:  
   \[
   \frac{-4}{2} = -2
   \]

2. **Simplify the \(x\)-terms**:  
   Use the rule of exponents \(\frac{x^m}{x^n} = x^{m-n}\):  
   \[
   \frac{x^8}{x^7} = x^{8-7} = x^1 = x
   \]

3. **Simplify the \(y\)-terms**:  
   Since the powers of \(y\) in both the numerator and denominator are the same (\(y^{10}\)), they cancel out:
   \[
   \frac{y^{10}}{y^{10}} = 1
   \]

Now, putting everything together:
\[
-2x \cdot 1 = -2x
\]

So, the simplified expression is:

\[
-2x
\]

Would you like more details or have any questions?

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Here are 5 questions related to the topic:
1. How do you simplify expressions with different powers of variables in the numerator and denominator?
2. What happens when the exponents of a variable in the numerator and denominator are equal?
3. How do negative exponents affect the simplification of terms?
4. Can you simplify the expression if additional variables are introduced in both numerator and denominator?
5. How do the rules of exponents apply when multiplying and dividing expressions?

**Tip**: Always remember to handle coefficients and variable exponents separately when simplifying algebraic fractions.

Learn how to simplify the algebraic expression (-4x^8y^10) / (2x^7y^10) by applying exponent rules and simplifying coefficients. This step-by-step guide helps students understand the core concepts of algebra and exponent laws, ideal for Grades 8-10.

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