To simplify the expression \(- (b^{14})^{12}\), we start by applying the power of a power property of exponents, which states that \((a^m)^n = a^{m \cdot n}\).
1. Apply the property:
\[
- (b^{14})^{12} = - b^{14 \cdot 12}
\]
2. Calculate \(14 \cdot 12\):
\[
14 \cdot 12 = 168
\]
3. Now plug this back into the expression:
\[
- b^{168}
\]
However, we are not seeing a direct match with any of the multiple-choice answers. Let's take a look at the choices again to find the equivalent expression:
A. \(1b^3\) --> This is just \(b^3\) which is incorrect.
B. \(-b^3\) --> This is incorrect, since our exponent is not \(3\).
C. \(-b^{-3}\) --> This expression means \(-\frac{1}{b^3}\), which is also incorrect.
D. \(-b^{13}\) --> This is incorrect as well.
Based on our calculations, none of the provided answers match the simplified form of the expression \(- b^{168}\). There appears to be an error in the options provided, as none of them are equivalent to \(- (b^{14})^{12}\).
If you intended to ask about a different expression or there was an error with the exponent values, please clarify so that we can assist you better!