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.