To simplify the expression:

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

We will:

1. Simplify the coefficients: \(\frac{-4}{7}\) remains as \(-\frac{4}{7}\).
2. Simplify the \(x\)-terms: \(x^8 / x^7 = x^{8-7} = x^1 = x\).
3. Simplify the \(y\)-terms: \(y^{10} / y^{10} = 1\).

Now, the simplified expression becomes:

\[
-\frac{4x}{7}
\]

Let me know if you'd like more details or further explanation!

Here are 5 related questions to expand on this:
1. How do you simplify expressions with negative exponents?
2. What happens when you divide variables raised to the same power?
3. How do you simplify fractions with variables in both the numerator and denominator?
4. Can you apply the same rules to expressions with more variables, like \(x^m y^n\)?
5. How do you simplify when there's subtraction in the exponents, such as \(x^{a-b}\)?

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

Learn how to simplify the expression (-4x^8y^10)/(7x^7y^10) using the laws of exponents. This problem involves simplifying coefficients, variable terms, and exponent rules, making it suitable for students in Grades 7-10.

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