What is an equivalent expression for −(b1/4)12 ?(1 point)

\(-b^{1/3}\): This is not equivalent.
\(-b^{3}\): This is also not equivalent.
\(-b^{-3}\): This means \(-\frac{1}{b^{3}}\), which is not equivalent.
\(\frac{1}{b^{3}}\): This is also not equivalent.

Question

-b1/3
-b^3
-b^-3
1/b^3

GPT-4o mini · Answer

To simplify the expression $-\left(\frac{b}{4}\right)^{12}$, we'll analyze what's given: 1. The expression $-\left(\frac{b}{4}\right)^{12}$ can be rewritten as: $$ -\frac{b^{12}}{4^{12}} = -\frac{b^{12}}{(2^2)^{12}} = -\frac{b^{12}}{2^{24}} $$ Now, let's evaluate the options provided: 1. **$-b^{1/3}$**: This is not equivalent. 2. **$-b^{3}$**: This is also not equivalent. 3. **$-b^{-3}$**: This means $-\frac{1}{b^{3}}$, which is not equivalent. 4. **$\frac{1}{b^{3}}$**: This is also not equivalent. None of the choices provided are equivalent to $-\left(\frac{b}{4}\right)^{12}$. Based on the given answer choices, it looks like there might be a misunderstanding since none align with the calculations from the expression. Therefore, the equivalent expression for $-\left(\frac{b}{4}\right)^{12}$ is not directly present in the options provided. Could you please verify the options?