https://file.aiquickdraw.com/mathbot/file/17293486178285hbl9s3s.jpg

Let's analyze the expression given in the image:

\[
\left( \frac{w^{-2}x^4z^6}{w^{-3}x^2z^8} \right)^{-3}
\]

### Step-by-Step Simplification:

1. **Simplify the expression inside the parentheses**:

   Using the property of exponents \( \frac{a^m}{a^n} = a^{m-n} \):

   \[
   \frac{w^{-2}}{w^{-3}} = w^{-2 - (-3)} = w^{-2 + 3} = w^1 = w
   \]
   
   \[
   \frac{x^4}{x^2} = x^{4-2} = x^2
   \]
   
   \[
   \frac{z^6}{z^8} = z^{6-8} = z^{-2}
   \]

   So, the expression becomes:

   \[
   (w \cdot x^2 \cdot z^{-2})^{-3}
   \]

2. **Apply the outer exponent \(-3\)**:

   Use the property \( (a^m)^n = a^{m \cdot n} \). Distribute the \(-3\) to all terms inside:

   \[
   w^{-3} \cdot x^{-6} \cdot z^{6}
   \]

3. **Final expression**:

   The simplified expression is:

   \[
   \frac{z^6}{w^3 x^6}
   \]

### Correct Answer:
Looking at the options, the answer is (D):

\[
\frac{z^6}{w^3 x^6}
\]

---

Would you like further explanation or details on any step?

Here are five related questions to explore further:

1. How do you simplify expressions with negative exponents?
2. What are the rules for multiplying exponents?
3. How do you handle fractional exponents in simplification?
4. Can you apply the same exponent rules to expressions with more variables?
5. How would you solve similar expressions if there are more complex terms?

**Tip:** When simplifying expressions, always work from the inside out and apply exponent rules carefully!

Simplify the expression (w^-2 x^4 z^6 / w^-3 x^2 z^8)^-3 and write the answers in positive exponents.

Learn how to simplify the expression (w^-2 x^4 z^6 / w^-3 x^2 z^8)^-3 using exponent rules, and write the result with positive exponents. This problem involves algebraic simplification with exponent properties and is suitable for students in Grades 8-10.

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