To determine which expression simplifies to have a positive exponent, let's analyze each option step by step.
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Expression: \(-2(-3)^2\) \[ = -2 \times 9 = -18 \quad \text{(no exponents)} \]
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Expression: \(3^{-3} + 3^{-4}\) Factoring out the smallest exponent: \[ = 3^{-4}(3^1 + 1) = 3^{-4}(3 + 1) = 3^{-4} \times 4 \quad \text{(still has negative exponent)} \]
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Expression: \(3^2 (3^{-5})\) Using the exponent rule \(a^m \cdot a^n = a^{m+n}\): \[ = 3^{2 + (-5)} = 3^{-3} \quad \text{(still has negative exponent)} \]
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Expression: \(\frac{3^{-11}}{3^{-7}}\) Using the exponent rule \(\frac{a^m}{a^n} = a^{m-n}\): \[ = 3^{-11 - (-7)} = 3^{-11 + 7} = 3^{-4} \quad \text{(still has negative exponent)} \]
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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.
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