https://file.aiquickdraw.com/mathbot/file/1730305266113evmj8ps9.jpg

The expression in the image is:

\[
(x^{-3} y^{-1})(x^{-3} y^{0} y^2)
\]

To simplify this, we can proceed as follows:

1. **Separate the Terms**:
   \[
   (x^{-3} y^{-1})(x^{-3} y^{0} y^2) = x^{-3} y^{-1} \cdot x^{-3} \cdot y^{0} \cdot y^2
   \]

2. **Combine Like Terms**:
   Use the rule \( a^m \cdot a^n = a^{m+n} \) for each variable:
   
   - For \( x \): \( x^{-3} \cdot x^{-3} = x^{-3-3} = x^{-6} \)
   - For \( y \): \( y^{-1} \cdot y^{0} \cdot y^2 = y^{-1+0+2} = y^{1} \)

3. **Write the Result**:
   \[
   x^{-6} y^{1} = \frac{y}{x^6}
   \]

Thus, the simplified form of the expression is:

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

Would you like more details on any of these steps?

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Here are 5 related questions to expand on this concept:

1. How do you simplify expressions involving negative exponents?
2. What does \( y^0 \) represent, and why is it equal to 1?
3. How would the expression change if the exponents of \( x \) and \( y \) were positive instead?
4. How do you handle variables raised to zero in any algebraic expression?
5. Can the process of simplifying exponent expressions be applied to any base, not just variables?

**Tip:** When multiplying terms with the same base, always add the exponents—this simplifies complex expressions quickly.

Learn how to simplify the expression (x^(-3) y^(-1))(x^(-3) y^0 y^2) by applying exponent rules, including handling negative and zero exponents. This solution provides step-by-step guidance suitable for students in Grades 8-10.

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