https://file.aiquickdraw.com/mathbot/file/1726026089236lw2z4bhu.jpg

Let's simplify the given expression:

\[
\frac{x^8 \cdot x^4 \cdot y^{-5} \cdot y^{-2}}{1}
\]

1. **Combine the terms with the same base:**

   For the \(x\) terms: 
   \[
   x^8 \cdot x^4 = x^{8+4} = x^{12}
   \]

   For the \(y\) terms:
   \[
   y^{-5} \cdot y^{-2} = y^{-5 + (-2)} = y^{-7}
   \]

2. The simplified expression is:
   \[
   x^{12} \cdot y^{-7}
   \]

Since dividing by 1 does not change the value, the final equivalent expression is:

\[
x^{12} \cdot y^{-7}
\]

Let me know if you need further details or explanations!

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Here are 5 related questions:
1. How do you simplify expressions with negative exponents?
2. What is the rule for multiplying powers with the same base?
3. How do you handle division with exponents?
4. How do you rewrite \(y^{-7}\) as a positive exponent?
5. Can you apply these rules to expressions involving more variables?

**Tip:** To simplify expressions, always handle like terms first (e.g., same base) and apply the exponent rules carefully!

Select the equivalent expression: (x^8 * x^4 * y^-5 * y^-2) / 1

Simplify the expression (x^8 * x^4 * y^-5 * y^-2) using exponent rules. This step-by-step solution demonstrates how to combine like terms and apply the laws of exponents. Ideal for students in Grades 8-10.

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