https://file.aiquickdraw.com/mathbot/file/1727793588599m3o5zy9o.jpg

Let's fully simplify the expression:

\[
\frac{6w^8x^4}{3w^2x^{12}}
\]

### Step-by-Step Simplification:

1. **Simplify the coefficients**: 
   \[
   \frac{6}{3} = 2
   \]

2. **Simplify the powers of \( w \)**:
   Use the rule for division of powers with the same base: \( \frac{a^m}{a^n} = a^{m-n} \).
   \[
   \frac{w^8}{w^2} = w^{8-2} = w^6
   \]

3. **Simplify the powers of \( x \)**:
   Similarly, apply the division of powers rule:
   \[
   \frac{x^4}{x^{12}} = x^{4-12} = x^{-8}
   \]
   Since negative indices are not allowed, rewrite this as:
   \[
   x^{-8} = \frac{1}{x^8}
   \]

4. **Combine everything**:
   \[
   \frac{6w^8x^4}{3w^2x^{12}} = 2w^6 \times \frac{1}{x^8} = \frac{2w^6}{x^8}
   \]

### Final Answer:
\[
\frac{2w^6}{x^8}
\]

Would you like further details or have any questions?

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Here are 5 related questions to further expand on this topic:
1. How do you simplify expressions with variables raised to negative exponents?
2. What happens if there is a zero exponent in any of the terms?
3. How do you simplify expressions with multiple variables?
4. How do you simplify expressions with fractional exponents?
5. What is the rule for raising a power to another power?

**Tip**: Always remember that negative exponents can be rewritten as fractions, which simplifies the expression further!

Fully simplify the expression: \(\frac{6w^8x^4}{3w^2x^{12}}\). Give your answer without any negative indices.

Learn how to fully simplify the expression \(\frac{6w^8x^4}{3w^2x^{12}}\) by applying exponent rules. This problem is suitable for students in Grades 8-10 and involves concepts such as division of powers and negative exponents.

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