To simplify the expression \(- (b^{14})^{12}\), we use the power of a power property, which states that \((a^m)^n = a^{m \cdot n}\).
So, \(- (b^{14})^{12} = - b^{14 \cdot 12} = - b^{168}\).
Now, looking at the options provided:
A. \(1/b^3\)
B. \(-b^3\)
C. \(-b^{-3}\)
D. \(-b^{13}\)
None of these options are equivalent to \(-b^{168}\).
It seems there may be a misunderstanding or a mistake in the options provided; none of the options correctly simplify to \(- (b^{14})^{12}\).
However, if you meant to simplify \(-(b^{14})^{-\frac{1}{2}}\), it would yield:
\[
-(b^{14})^{-\frac{1}{2}} = -b^{14 \cdot -\frac{1}{2}} = -b^{-7} = -\frac{1}{b^7}
\]
But based on your original expression, the simplified form is indeed \(-b^{168}\), which is not provided in your options. Please double-check the original expression or the options given.