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To simplify the expression \(-\left(b^{1/4}\right)^{12}\), we can use the property of exponents that states \((x^m)^n = x^{m \cdot n}\).
Applying this property:
\[
\left(b^{1/4}\right)^{12} = b^{(1/4) \cdot 12} = b^{12/4} = b^3
\]
Then, considering the negative sign outside the parentheses:
\[
-(b^{1/4})^{12} = -b^3
\]
Thus, the equivalent expression is \(-b^3\).
From the provided responses, the correct answer is:
**−b3 (negative b cubed)**.