To determine which expression simplifies to a positive exponent, let's simplify each option one by one.
A. \(-2 (-3)^2\)
- Calculate \((-3)^2 = 9\)
- Expression becomes \(-2 \cdot 9 = -18\), which doesn't have any exponent form.
B. \(3^{-3} + 3^{-4}\)
- Combine the terms. The least power is \(3^{-4}\): \[ 3^{-3} + 3^{-4} = 3^{-4}(3^1 + 1) = 3^{-4}(3 + 1) = 3^{-4} \cdot 4 \]
- The simplified expression is \(4 \cdot 3^{-4}\), which still has a negative exponent.
C. \(3^2 (3^{-5})\)
- Combine the exponents: \[ 3^2 \cdot 3^{-5} = 3^{2 + (-5)} = 3^{-3} \]
- This has a negative exponent.
D. \(\frac{3^{-11}}{3^{-7}}\)
- Subtract the exponents in division: \[ 3^{-11 - (-7)} = 3^{-11 + 7} = 3^{-4} \]
- This also has a negative exponent.
Now, let's summarize:
- A leaves no exponent form.
- B simplifies to a negative exponent.
- C simplifies to a negative exponent.
- D simplifies to a negative exponent.
None of the provided options \(A\), \(B\), \(C\), or \(D\) simplify to a positive exponent.
Given the mathematical operations, none of these expressions will yield a positive exponent when simplified. If strictly looking for an option that yields a positive exponent, none suffice in this context.