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To simplify the expression \( 37 \cdot 3^{-9} \) using the properties of exponents, follow these steps:
1. **Recall the property of negative exponents**: \( a^{-n} = \frac{1}{a^n} \).
Applying this to \( 3^{-9} \):
\[
3^{-9} = \frac{1}{3^9}
\]
2. **Substitute this back into the expression**:
\[
37 \cdot 3^{-9} = 37 \cdot \frac{1}{3^9} = \frac{37}{3^9}
\]
3. **Now, calculate \( 3^9 \)**:
\[
3^9 = 19683
\]
4. **Substitute \( 3^9 \) back into the expression**:
\[
\frac{37}{3^9} = \frac{37}{19683}
\]
Thus, the simplified expression with only positive exponents is:
\[
\frac{37}{19683}
\]
Final answer: \(\frac{37}{19683}\)