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

Answer 1

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