https://file.aiquickdraw.com/mathbot/file/1729124689271d8fvka4z.jpg

The expression in the image is:

\[
\frac{8x^2y^4}{2x^8y^4}
\]

### Step-by-Step Simplification:

1. **Simplify the coefficients (numbers):**
   \[
   \frac{8}{2} = 4
   \]
   So, the expression becomes:
   \[
   4 \cdot \frac{x^2y^4}{x^8y^4}
   \]

2. **Simplify the powers of \( x \):**
   \[
   \frac{x^2}{x^8} = x^{2 - 8} = x^{-6}
   \]
   So, the expression now becomes:
   \[
   4 \cdot x^{-6} \cdot \frac{y^4}{y^4}
   \]

3. **Simplify the powers of \( y \):**
   \[
   \frac{y^4}{y^4} = 1
   \]
   This simplifies the expression to:
   \[
   4x^{-6}
   \]

4. **Rewrite using positive exponents:**
   Since \( x^{-6} \) is the same as \( \frac{1}{x^6} \), the final expression becomes:
   \[
   \frac{4}{x^6}
   \]

### Final Answer:
\[
\frac{4}{x^6}
\]

Let me know if you need further details or explanations!

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Here are 5 related questions to deepen your understanding:

1. How do you simplify expressions with both negative and positive exponents?
2. What happens when the exponents of the variables are the same in the numerator and denominator?
3. How can you rewrite expressions involving negative exponents in a different form?
4. How do you apply the rules of exponents when variables are involved?
5. What is the significance of keeping exponents positive in the final answer?

**Tip:** Always subtract the exponents of like terms in a fraction, and remember to convert negative exponents by moving the base to the denominator.

Simplify the expression \( \frac{8x^2y^4}{2x^8y^4} \) using only positive exponents.

Learn how to simplify the exponential expression \( \frac{8x^2y^4}{2x^8y^4} \) step by step using the laws of exponents. This problem covers key algebraic concepts, such as simplifying variables and coefficients, and understanding negative exponents. Suitable for Grades 7-9 students.

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