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

Question

?(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.