The expression \(\frac{x^{-7}}{y^{-2}}\) can be simplified using the properties of exponents. Specifically, we use the rule that \(a^{-n} = \frac{1}{a^n}\) and that \(\frac{a^{-m}}{b^{-n}} = \frac{b^n}{a^m}\).

Let's simplify step by step:

\[
\frac{x^{-7}}{y^{-2}} = \frac{1}{x^7} \times y^2 = \frac{y^2}{x^7}
\]

So, the simplified expression is:

\[
\frac{y^2}{x^7}
\]

Do you want more details or have any questions?

Here are 5 related questions:
1. How would you simplify the expression \(\frac{a^{-3}}{b^{-4}}\)?
2. What is the value of \(x^{-3} \times x^5\)?
3. How do you simplify \(\frac{2x^{-4}y^{-1}}{z^{-3}}\)?
4. What happens if both the numerator and denominator have positive exponents in the expression \(\frac{a^m}{b^n}\)?
5. How do you simplify \(\frac{p^{-1}q^2}{r^{-3}s^{-4}}\)?

**Tip:** When dealing with negative exponents, remember that you can rewrite them as positive exponents by taking the reciprocal.

Learn how to simplify the expression \(\frac{x^{-7}}{y^{-2}}\) step-by-step with exponent rules. This problem covers key concepts in exponents and fractional exponents. Suitable for students in Grades 7-9.

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