Apply All Exponent Rules Practice Complete this assessment to review what you've learned. It will not count toward your grade. 1 of 51 of 5 Items Question Apply the Properties of Integer Exponents to generate equivalent expressions to 37⋅3−9 with only positive exponents, then solve the expression. Your answer will be a simplified fraction with no remaining exponents.(1 point) 37⋅3−9= Remaining Attempts : 3 Skip to navigation

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: \(\frac{37}{19683}\)