Question

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

−b3
negative b cubed

−b−3
negative b superscript negative 3 baseline

1b3
Start Fraction 1 over b cubed End Fraction

−b13

Answer 1

To simplify the expression \(-\left(\frac{b}{4}\right)^{12}\), we follow these steps:

1. Simplify \(\left(\frac{b}{4}\right)^{12}\):
\[
\left(\frac{b}{4}\right)^{12} = \frac{b^{12}}{4^{12}} = \frac{b^{12}}{(2^2)^{12}} = \frac{b^{12}}{2^{24}}.
\]

2. Now, apply the negative sign:
\[
-\left(\frac{b}{4}\right)^{12} = -\frac{b^{12}}{2^{24}}.
\]

To find equivalent expressions among the given options, we can write \( \frac{1}{b^3} \) as \( b^{-3} \), but none of the simplifications step directly lead to the candidates provided without further letter manipulation or conversions.

But based on what is provided:

1. **−b^3** is not equivalent.
2. **−b^−3** is also not equivalent.
3. **1/b^3** is not directly corresponding to \(-\left(\frac{b}{4}\right)^{12}\).
4. **−b^{13}** does not match either.

Hence, if we examine the expressions given, we should correctly focus on evaluating the \(-\frac{b^{12}}{2^{24}}\) expression.

None of the options provided would truly represent the simplified \(-\left(\frac{b}{4}\right)^{12}\) expression correctly.

However, if there's a typographical or interpretive adjustment that aligns broader with traditional expressive forms, “negative b cubed" and “negative b superscript negative 3 baseline” could have targeted values based on ambiguous understanding, but the closest simplified form is indeed:

\(-\frac{b^{12}}{2^{24}}\) which is not clearly represented within the above options.

If forced to select based on potential common misinterpretations, **−b^−3** could theoretically misconstrue certain setups of expression yet retains none if strictly formatting simplistically. Thus, proceed to reconsider the equality foresights or extend question context, retaining broader algebra awareness.