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

(1 point)
Responses

−b13
negative b raised to the 1 third power

−b−3
negative b to the negative 3 power

b4
b to the 4th power

−b3

Answer 1

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

Here’s the step-by-step simplification:

1. Apply the property:
\[
- (b^{14})^{12} = - b^{14 \cdot 12} = - b^{168}
\]

Now, looking at the options:

1. \(-b^{13}\) (which is incorrect)
2. \(-b^{-3}\) (which is incorrect)
3. \(b^{4}\) (which is incorrect)
4. \(-b^{3}\) (which is incorrect)

None of the provided responses are equivalent to the expression we simplified, which is \(-b^{168}\).

Let me know if there is anything else you need!