https://file.aiquickdraw.com/mathbot/file/1725464996083cb2uh9cv.jpg

The expression in the image appears to be:

\[
\frac{8y}{2y^3}
\]

To simplify this expression, we can divide the coefficients and subtract the exponents of like terms.

### Step-by-Step Solution:

1. **Divide the coefficients:**
   \[
   \frac{8}{2} = 4
   \]

2. **Subtract the exponents of \( y \):**
   \[
   y^{1 - 3} = y^{-2}
   \]

3. **Combine the results:**
   \[
   \frac{8y}{2y^3} = 4y^{-2}
   \]

4. **Express with a positive exponent:**
   \[
   4y^{-2} = \frac{4}{y^2}
   \]

### Final Simplified Expression:

\[
\frac{8y}{2y^3} = \frac{4}{y^2}
\]

Would you like more details or have any questions about this solution?

### Related Questions to Explore:

1. What are the rules for dividing exponents with the same base?
2. How do negative exponents affect the simplification of algebraic expressions?
3. How would you handle the expression if it were a fraction within a fraction?
4. Can you simplify other similar expressions, such as \(\frac{10x^2}{5x^4}\)?
5. How does this process change if we have different variables in the numerator and the denominator?

**Tip:** Always look for common factors in the numerator and denominator to simplify fractions effectively.

Discover how to simplify the algebraic expression 8y / 2y^3. This solution involves dividing coefficients and applying exponent rules, making it perfect for students in Grades 9-10.

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