To simplify the expression \(-\left(\frac{b}{4}\right)^{12}\), we follow these steps:
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Simplify \(\left(\frac{b}{4}\right)^{12}\): \[ \left(\frac{b}{4}\right)^{12} = \frac{b^{12}}{4^{12}} = \frac{b^{12}}{(2^2)^{12}} = \frac{b^{12}}{2^{24}}. \]
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Now, apply the negative sign: \[ -\left(\frac{b}{4}\right)^{12} = -\frac{b^{12}}{2^{24}}. \]
To find equivalent expressions among the given options, we can write \( \frac{1}{b^3} \) as \( b^{-3} \), but none of the simplifications step directly lead to the candidates provided without further letter manipulation or conversions.
But based on what is provided:
- −b^3 is not equivalent.
- −b^−3 is also not equivalent.
- 1/b^3 is not directly corresponding to \(-\left(\frac{b}{4}\right)^{12}\).
- −b^{13} does not match either.
Hence, if we examine the expressions given, we should correctly focus on evaluating the \(-\frac{b^{12}}{2^{24}}\) expression.
None of the options provided would truly represent the simplified \(-\left(\frac{b}{4}\right)^{12}\) expression correctly.
However, if there's a typographical or interpretive adjustment that aligns broader with traditional expressive forms, “negative b cubed" and “negative b superscript negative 3 baseline” could have targeted values based on ambiguous understanding, but the closest simplified form is indeed:
\(-\frac{b^{12}}{2^{24}}\) which is not clearly represented within the above options.
If forced to select based on potential common misinterpretations, −b^−3 could theoretically misconstrue certain setups of expression yet retains none if strictly formatting simplistically. Thus, proceed to reconsider the equality foresights or extend question context, retaining broader algebra awareness.