Question

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

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

−b−3
negative b superscript negative 3 baseline

1b3
Start Fraction 1 over b cubed End Fraction

−b3

Answer 1

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

Applying this property:

\[
-(b^{14})^{12} = -b^{(14 \cdot 12)} = -b^{168}
\]

None of the provided responses match \(-b^{168}\). However, let's examine the options given:

1. \(-b^{13}\)
2. \(-b^{-\frac{1}{3}}\)
3. \(\frac{1}{b^3}\)
4. \(-b^{3}\)

None of these options are equivalent to \(-b^{168}\). Therefore, it seems there might be an error with the options provided. The equivalent expression for \(- (b^{14})^{12}\) is \(-b^{168}\), which is not listed among the responses.