Question

What is an equivalent expression for −(b^1/4)^12
?(1 point)
Responses

1b3
Start Fraction 1 over b cubed End Fraction

−b−3
negative b superscript negative 3 baseline

−b3
negative b cubed

−b13

Answer 1

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)**.