To simplify the expression \(-\left(\frac{b}{4}\right)^{12}\), we follow these steps:
1. Simplify \(\left(\frac{b}{4}\right)^{12}\):
\[
\left(\frac{b}{4}\right)^{12} = \frac{b^{12}}{4^{12}} = \frac{b^{12}}{(2^2)^{12}} = \frac{b^{12}}{2^{24}}.
\]
2. 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:
1. **−b^3** is not equivalent.
2. **−b^−3** is also not equivalent.
3. **1/b^3** is not directly corresponding to \(-\left(\frac{b}{4}\right)^{12}\).
4. **−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.