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

Question

Responses

−b−3
negative b superscript negative 3 baseline

1/b3
Start Fraction 1 over b cubed End Fraction

−b1/3
negative b superscript Start Fraction 1 over 3 End Fraction baseline

−b3

Answer 1

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

Here, we can multiply the exponents:

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

Calculating \((1/4) \cdot 12\):

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

Thus, the expression simplifies to:

\[ -b^3 \]

So, an equivalent expression for \(- (b^{1/4})^{12}\) is:

\(-b^3\)

Therefore, the correct response is:

\(-b^3\)