To simplify the expression \(-\left(\frac{b}{4}\right)^{12}\), we will execute the exponent first.
Let's start with the base inside the parentheses:
\[ \left(\frac{b}{4}\right)^{12} = \frac{b^{12}}{4^{12}} \]
Now, substituting back, we have:
\[ -(\frac{b^{12}}{4^{12}}) = -\frac{b^{12}}{4^{12}} \]
Next, let's identify \(4^{12}\):
\[ 4^{12} = (2^2)^{12} = 2^{24} \]
So the expression becomes:
\[ -\frac{b^{12}}{2^{24}} \]
To express \(\frac{b^{12}}{2^{24}}\) in a different way, we use the negative sign outside to change the exponent:
\[ -\frac{1}{b^{-12}} \text{ or } -b^{12} \cdot 2^{-24} \]
However, the choices you have given don’t correspond to the simplification we conducted.
Now let's take a look at your answer options:
- \(-b^{1/3}\)
- \(-b^3\)
- \(-b^{-3}\)
- \(\frac{1}{b^3}\)
The original expression in terms of its complete form does not seem to match directly with any of those options.
However, if the expression required was instead \(-b^{12}\) or if any transformation was initiated from there, I can clarify further.
To conclude: none of the answer choices here, based on the expression \(-\left(\frac{b}{4}\right)^{12}\), appear equivalent. Would you like to check the original requirements if there were arithmetic operations requested on a different form or recheck the problem?