What is an equivalent expression for −(b14)12

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

So, \(- (b^{14})^{12} = - b^{14 \cdot 12} = - b^{168}\).

Now, looking at the options provided:

A. \(1/b^3\)
B. \(-b^3\)
C. \(-b^{-3}\)
D. \(-b^{13}\)

None of these options are equivalent to \(-b^{168}\).

It seems there may be a misunderstanding or a mistake in the options provided; none of the options correctly simplify to \(- (b^{14})^{12}\).

However, if you meant to simplify \(-(b^{14})^{-\frac{1}{2}}\), it would yield:

\[
-(b^{14})^{-\frac{1}{2}} = -b^{14 \cdot -\frac{1}{2}} = -b^{-7} = -\frac{1}{b^7}
\]

But based on your original expression, the simplified form is indeed \(-b^{168}\), which is not provided in your options. Please double-check the original expression or the options given.

answer

Let's clarify and find the equivalent expression for \(- (b^{14})^{12}\).

Starting with the expression:
\[
-(b^{14})^{12}
\]

Using the power of a power property:
\[
-(b^{14})^{12} = -b^{14 \cdot 12} = -b^{168}
\]

Now let's compare that with the answer choices provided:

A. \(1/b^3\)
B. \(-b^3\)
C. \(-b^{-3}\)
D. \(-b^{13}\)

None of these options, unfortunately, represent \(-b^{168}\).

If you're looking specifically for options among those listed, here’s the takeaway:
- The correct simplified expression for \(- (b^{14})^{12}\) is \(-b^{168}\), which is not included in the answer choices.

If you have any further details or need to refer to a different expression, please let me know!