To simplify the expression \(- (b^{14})^{12}\), we can apply the power of a power rule in exponentiation, which states that \((a^m)^n = a^{m \cdot n}\).
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First, multiply the exponents: \[ (b^{14})^{12} = b^{14 \cdot 12} = b^{168} \]
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Now, apply the negative sign: \[
- (b^{168}) = -b^{168} \]
Since none of the options match \(-b^{168}\), let's consider what the question might be asking for based on the original response options.
If the question was about a different expression, specifically \(- (b^{14})^{-12}\), the computation would be:
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Apply the negative exponent rule: \[ (b^{14})^{-12} = \frac{1}{(b^{14})^{12}} = \frac{1}{b^{168}} \]
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Add the negative sign: \[
- (b^{14})^{-12} = - \frac{1}{b^{168}} \]
Given your options, the closest match based on these interpretations is likely misleading due to how we interpreted the expression:
- 1b³ is not equivalent.
- -b³ is not equivalent.
- -b13 is not equivalent.
- -b−3 is not equivalent.
None of the provided responses correctly match the equivalent expression for \(- (b^{14})^{12}\) or \(- (b^{14})^{-12}\). If you meant \(- (b^{14})^{-12}\), please confirm for clarification. Based on the initial expression, the derived simplification is \(-b^{168}\).
If you need further clarifications or details, feel free to ask!