https://file.aiquickdraw.com/mathbot/file/1726755035383bk97zqo1.jpg

The expression shown in the image is:

\[
x^{-8} \cdot y^3
\]

This is a multiplication of two terms: \(x^{-8}\) and \(y^3\). There's no further simplification to do unless you have additional context (like values for \(x\) or \(y\)).

If you want the final answer in terms of \(x\) and \(y\), it remains:

\[
x^{-8} \cdot y^3
\]

However, you can rewrite \(x^{-8}\) using positive exponents as:

\[
\frac{y^3}{x^8}
\]

Let me know if you'd like further clarification or have specific operations to apply.

Would you like to explore similar expressions or manipulations? Here are 5 questions to help deepen your understanding:

1. How would the expression change if the powers were different (e.g., \(x^{-2}\) and \(y^4\))?
2. Can you simplify \(x^{-8} \cdot y^{-3}\)?
3. How do negative exponents work, and why does \(x^{-n} = \frac{1}{x^n}\)?
4. What happens if \(x = 0\) or \(y = 0\) in expressions with exponents?
5. How do you multiply two expressions with negative exponents, like \(x^{-2} \cdot x^{-3}\)?

**Tip:** When working with negative exponents, you can always rewrite them as fractions for easier manipulation!

Understand how to handle the multiplication of variables with exponents in the expression x^-8 * y^3. This explanation includes the application of negative exponent rules and simplifies the expression to y^3/x^8, suitable for students in Grades 7-9.

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