https://file.aiquickdraw.com/mathbot/file/1725497155473toq07kf5.jpg

Let's solve the expression shown in the image step by step.

The expression appears to be:

\[
\frac{(8xy)^{-2}}{xy} \cdot \frac{x^{-5}}{y^{-1}}
\]

### Step 1: Simplify each component

1. **Simplify \((8xy)^{-2}\):**
   \[
   (8xy)^{-2} = \frac{1}{(8xy)^2} = \frac{1}{64x^2y^2}
   \]

2. **Simplify \(\frac{(8xy)^{-2}}{xy}\):**
   \[
   \frac{\frac{1}{64x^2y^2}}{xy} = \frac{1}{64x^2y^2} \cdot \frac{1}{xy} = \frac{1}{64x^3y^3}
   \]

3. **Simplify \(\frac{x^{-5}}{y^{-1}}\):**
   \[
   \frac{x^{-5}}{y^{-1}} = x^{-5} \cdot y^1 = \frac{y}{x^5}
   \]

### Step 2: Multiply the simplified terms together
Now, multiply the results from Step 1:

\[
\frac{1}{64x^3y^3} \cdot \frac{y}{x^5} = \frac{y}{64x^8y^3} = \frac{1}{64x^8y^2}
\]

### Final Answer
The simplified expression is:

\[
\frac{1}{64x^8y^2}
\]

Would you like more details or have any questions?

### Related Questions:
1. How would the expression change if the exponent on \(x^{-5}\) was different?
2. What happens if the base in \((8xy)^{-2}\) is modified to \(8x^2y\)?
3. Can you simplify \(\frac{(2x)^{-3}}{x^2} \cdot \frac{y^{-4}}{y}\)?
4. What would the steps be to simplify \(\frac{(3ab)^{-2}}{a^2b^2} \cdot \frac{a^{-3}}{b^{-2}}\)?
5. How does the process differ if we have fractional exponents?

### Tip:
Always simplify the exponents step by step and combine like terms to ensure accuracy.

Simplify the expression: (8xy)^{-2} / xy * x^{-5} / y^{-1}.

Learn how to simplify the algebraic expression (8xy)^{-2} / xy * x^{-5} / y^{-1} step-by-step. This solution covers exponent rules and simplifies the expression to 1 / 64x^8y^2, making it easier for students in Grades 9-11 to understand.

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