To generate an equivalent expression using only positive exponents, we can apply the properties of integer exponents.
The given expression is not mentioned in the question, so let's assume it is:
\[ 3^{-2} \cdot 5^4 \]
To apply the properties of integer exponents, we can use two main rules:
1. Product rule: \(a^m \cdot a^n = a^{m+n}\)
2. Power of a power rule: \((a^m)^n = a^{m \cdot n}\)
Using the product rule, we can rewrite the given expression as:
\[ \frac{1}{3^2} \cdot 5^4 \]
Next, we can simplify the expression using the power of a power rule. Since \(3^2\) is the same as \(3 \cdot 3\), we can rewrite it as:
\[ \frac{1}{3 \cdot 3} \cdot 5^4 \]
Simplifying further, we get:
\[ \frac{1}{9} \cdot 5^4 \]
Now, we can simplify the expression by multiplying:
\[ \frac{1}{9} \cdot 625 \]
Multiplying 1 by 625 and 9 by 1, we get:
\[ \frac{625}{9} \]
Therefore, the equivalent expression for \(3^{-2} \cdot 5^4\) using only positive exponents is \(\frac{625}{9}\).