Question Apply the Properties of Integer Exponents to generate equivalent expressions to (7^−3)^7 ⋅ 7^20/6^−2 with only positive exponents, then solve the expression. Provide the answer as an improper fraction.

To simplify the expression \( (7^{-3})^7 \cdot \frac{7^{20}}{6^{-2}} \) while only using positive exponents, we will apply the properties of integer exponents.

1. **Simplify \( (7^{-3})^7 \)**:
\[
(7^{-3})^7 = 7^{-3 \cdot 7} = 7^{-21}
\]

2. **Rewrite the expression**:
Now we rewrite the entire expression:
\[
7^{-21} \cdot \frac{7^{20}}{6^{-2}}
\]

3. **Distributing the division**:
Using the property of division of exponents, we can rewrite \( \frac{7^{20}}{6^{-2}} \) as:
\[
7^{20} \cdot 6^{2}
\]

4. **Combine the terms**:
Now, substitute back into our expression:
\[
7^{-21} \cdot 7^{20} \cdot 6^{2}
\]

Using the property \( a^m \cdot a^n = a^{m+n} \):
\[
7^{-21 + 20} \cdot 6^{2} = 7^{-1} \cdot 6^{2}
\]

5. **Convert to positive exponents**:
To express \( 7^{-1} \) with a positive exponent, we use the property \( a^{-n} = \frac{1}{a^n} \):
\[
\frac{6^{2}}{7^{1}} = \frac{6^2}{7}
\]

6. **Calculate \( 6^{2} \)**:
\[
6^2 = 36
\]

7. **Final expression**:
Thus, we have:
\[
\frac{36}{7}
\]

So, the answer as an improper fraction is:
\[
\boxed{\frac{36}{7}}
\]