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The image contains an algebraic expression that asks to simplify the given fraction using positive exponents only. The expression to simplify is:

\[
\frac{20x^{7}y^{-12}}{25x^{2}y^{8}}
\]

Let's go through the steps of simplifying it:

### Step-by-step Simplification:

1. **Coefficients (numerical values):**
   \[
   \frac{20}{25} = \frac{4}{5}
   \]

2. **Exponents for \(x\):**
   Apply the quotient rule: \( \frac{x^7}{x^2} = x^{7-2} = x^5 \).

3. **Exponents for \(y\):**
   Apply the quotient rule: \( \frac{y^{-12}}{y^8} = y^{-12-8} = y^{-20} \).
   Since we want only positive exponents, move \( y^{-20} \) to the denominator: \( \frac{1}{y^{20}} \).

### Final Expression:
\[
\frac{4x^5}{5y^{20}}
\]

Thus, the simplified expression is \( \frac{4x^5}{5y^{20}} \), which corresponds to option D.

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Do you want further details or have any questions about this problem?  
Here are five related questions for further practice:

1. How do you simplify expressions with negative exponents in both the numerator and the denominator?
2. How can you use the quotient rule of exponents when both terms are in the denominator?
3. What is the process for converting a negative exponent into a positive exponent?
4. How does the quotient rule apply when both variables have coefficients?
5. Can you simplify a fraction if the exponents of the same base are equal?

**Tip:** Always simplify coefficients separately from the variable exponents when dealing with algebraic fractions.

Simplify the algebraic expression \(\frac{20x^{7}y^{-12}}{25x^{2}y^{8}}\) using only positive exponents.

Learn how to simplify the algebraic expression \(\frac{20x^{7}y^{-12}}{25x^{2}y^{8}}\) by using exponent rules and simplifying techniques. This detailed guide includes step-by-step simplifications, focusing on converting negative exponents to positive and reducing coefficients. Suitable for students in Grades 8-10.

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