Question

6. What is an equivalent expression for −(b14)12
?(2 points)
Responses

−b−3
negative b to the negative 3 power

−b3
negative b cubed

1b3
the fraction with numerator 1 and denominator b cubed

−1b3

Answer 1

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

So we have:

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

Now, we can express this with negative exponents. Recall that \(b^{-n} = \frac{1}{b^n}\), so:

\[
-b^{168} = -\frac{1}{b^{-168}}
\]

However, looking for an equivalent expression, we can see that none of the provided responses match \( -b^{168} \) or \( -\frac{1}{b^{168}} \).

Let’s analyze the provided options:

1. **−b−3**: This expression is equivalent to \(-\frac{1}{b^3}\) and does not match.
2. **−b3**: This expression is equivalent to \(-b^3\) and does not match.
3. **1b3**: This expression appears to be formatted incorrectly, but it suggests \(\frac{1}{b^3}\) and does not match.
4. **−1b3**: This also appears incorrect but would suggest \(-\frac{1}{b^3}\) and does not match.

None of the options given are equivalent to \(-(b^{14})^{12}\) or \( -b^{168} \).

However, if we were looking for a very simplified term, \(-b^{168}\) is the correct equivalent expression based on simplification, but it is not listed in your options.

Thus, please verify the details or check for any missed option. The correct answer from the information available would be:

\(-b^{168}\)

But since that is not provided, there seems to be a disconnect with the choices given.