Question

Question
What is an equivalent expression for −(b14)12
?(1 point)
Responses

1b3
Start Fraction 1 over b cubed End Fraction

−b3
negative b cubed

−b13
negative b superscript Start Fraction 1 over 3 End Fraction baseline

−b−3

Answer 1

To simplify the expression \(- (b^{14})^{12}\), we can apply the power of a power rule in exponentiation, which states that \((a^m)^n = a^{m \cdot n}\).

1. First, multiply the exponents:
\[
(b^{14})^{12} = b^{14 \cdot 12} = b^{168}
\]

2. Now, apply the negative sign:
\[
- (b^{168}) = -b^{168}
\]

Since none of the options match \(-b^{168}\), let's consider what the question might be asking for based on the original response options.

If the question was about a different expression, specifically \(- (b^{14})^{-12}\), the computation would be:

1. Apply the negative exponent rule:
\[
(b^{14})^{-12} = \frac{1}{(b^{14})^{12}} = \frac{1}{b^{168}}
\]

2. Add the negative sign:
\[
- (b^{14})^{-12} = - \frac{1}{b^{168}}
\]

Given your options, the closest match based on these interpretations is likely misleading due to how we interpreted the expression:

1. **1b³** is not equivalent.
2. **-b³** is not equivalent.
3. **-b13** is not equivalent.
4. **-b−3** is not equivalent.

None of the provided responses correctly match the equivalent expression for \(- (b^{14})^{12}\) or \(- (b^{14})^{-12}\). If you meant \(- (b^{14})^{-12}\), please confirm for clarification. Based on the initial expression, the derived simplification is \(-b^{168}\).

If you need further clarifications or details, feel free to ask!