Question

Which expression simplified would leave you with a positive exponent when simplified in exponent form?

-2(-3)^2

3^-3 + 3^-4

3^2 (3^-5)

3^-11/3^-7

3 (3^-5

Answer 1

To determine which expression simplifies to have a positive exponent, let's analyze each option step by step.

1. **Expression: \(-2(-3)^2\)**
\[
= -2 \times 9 = -18 \quad \text{(no exponents)}
\]

2. **Expression: \(3^{-3} + 3^{-4}\)**
Factoring out the smallest exponent:
\[
= 3^{-4}(3^1 + 1) = 3^{-4}(3 + 1) = 3^{-4} \times 4 \quad \text{(still has negative exponent)}
\]

3. **Expression: \(3^2 (3^{-5})\)**
Using the exponent rule \(a^m \cdot a^n = a^{m+n}\):
\[
= 3^{2 + (-5)} = 3^{-3} \quad \text{(still has negative exponent)}
\]

4. **Expression: \(\frac{3^{-11}}{3^{-7}}\)**
Using the exponent rule \(\frac{a^m}{a^n} = a^{m-n}\):
\[
= 3^{-11 - (-7)} = 3^{-11 + 7} = 3^{-4} \quad \text{(still has negative exponent)}
\]

5. **Expression: \(3(3^{-5})\)**
Again using the exponent rule:
\[
= 3^1 \cdot 3^{-5} = 3^{1 - 5} = 3^{-4} \quad \text{(still has negative exponent)}
\]

**Conclusion:**
None of the provided expressions simplify to a positive exponent. Each expression either results in a negative exponent or a constant without any exponent at all.