What is an equivalent expression for −(b exponent1/4)exponent12

To simplify the expression \(- (b^{1/4})^{12}\), we can use the power of a power property of exponents, which states that:

\[
(a^m)^n = a^{m \cdot n}
\]

Applying this property:

\[
-(b^{1/4})^{12} = -b^{(1/4) \cdot 12}
\]

Calculating the exponent:

\[
(1/4) \cdot 12 = 12/4 = 3
\]

So, we have:

\[
-(b^{1/4})^{12} = -b^3
\]

Therefore, the equivalent expression is:

\(-b^3\) (negative b cubed).