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

Question

Responses

−b^1/3
negative b superscript Start Fraction 1 over 3 End Fraction baseline

−b^−3
negative b superscript negative 3 baseline

−b^3
negative b cubed

1/b^3

Answer 1

To simplify the expression \(-(b^{1/4})^{12}\), we can use the property of exponents that states \((a^m)^n = a^{m \cdot n}\).

Let's apply this:

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

So, the equivalent expression for \(-(b^{1/4})^{12}\) is \(-b^3\).

Therefore, the correct response is:

−b^3 (negative b cubed)