https://file.aiquickdraw.com/mathbot/file/1730590480356rzm3xca7.jpg

The expression in the image is:

\[
\frac{x^{-4}}{y^{-6}}
\]

To simplify this, we can use the property of exponents that states \( a^{-n} = \frac{1}{a^n} \). This property also allows us to rewrite negative exponents in the denominator by moving them to the numerator (and vice versa).

Thus, we can rewrite the expression as follows:

\[
\frac{x^{-4}}{y^{-6}} = x^{-4} \cdot y^6 = \frac{y^6}{x^4}
\]

So, the simplified expression is:

\[
\frac{y^6}{x^4}
\]

Would you like further details or have any questions?

### Related Questions
1. How do we simplify expressions with multiple variables and negative exponents?
2. What happens if the exponent of \( x \) or \( y \) is positive instead of negative?
3. How can we rewrite \(\frac{x^4}{y^{-2}}\) in a simpler form?
4. How does the exponent rule apply to expressions with fractional exponents?
5. Can we apply the same exponent rules when there are radicals involved?

### Tip
Remember, any negative exponent can be turned positive by moving the base to the other side of a fraction.

Simplify the expression \( \frac{x^{-4}}{y^{-6}} \).

Learn how to simplify expressions with negative exponents, specifically \( \frac{x^{-4}}{y^{-6}} \). This problem covers algebraic concepts such as exponents and the negative exponent rule, making it suitable for students in Grades 8-10.

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