Question

Which expression simplified would leave you with a positive exponent when simplified in exponent form? (-2(-3) to the 2 power; 3 negative 3 power + 3 to the negative 4 power; 3 to the 2 power (3 negative 5 power); 3 to the negative 11 power divided 3 to the negative 7)

Answer 1

To determine which expression simplifies to leave a positive exponent, let's simplify each expression one at a time.

1. **Expression**: \(-2(-3)^{2}\)

Simplifying:
\[
-2 \cdot 9 = -18
\]
This is a negative number (not an exponent).

2. **Expression**: \(3^{-3} + 3^{-4}\)

To simplify this, we need a common base:
\[
= 3^{-3} + 3^{-4} = 3^{-4}(3^{1} + 1) = 3^{-4}(3 + 1) = 3^{-4} \cdot 4
\]
This results in \(4 \cdot 3^{-4}\), which is not a positive exponent.

3. **Expression**: \(3^{2} \cdot 3^{-5}\)

Using the properties of exponents:
\[
3^{2 + (-5)} = 3^{-3}
\]
This results in \(3^{-3}\), which is still a negative exponent.

4. **Expression**: \(\frac{3^{-11}}{3^{-7}}\)

Using the properties of exponents:
\[
3^{-11 - (-7)} = 3^{-11 + 7} = 3^{-4}
\]
This results in \(3^{-4}\), which is also a negative exponent.

### Conclusion:
None of the four expressions simplify to a positive exponent. They all result in negative exponents or negative results when calculated.