Question

What is an equivalent expression for −(b1/4)12 ?(1 point)
-b1/3
-b^3
-b^-3
1/b^3

Answer 1

To simplify the expression \(-\left(\frac{b^1}{4}\right)^{12}\):

1. **Apply the exponent:** When raising a fraction to an exponent, you can apply the exponent to both the numerator and the denominator:
\[
-\left(\frac{b^1}{4}\right)^{12} = -\frac{(b^1)^{12}}{4^{12}} = -\frac{b^{12}}{4^{12}}
\]

2. **Rewrite \(4^{12}\):**
\[
4^{12} = (2^2)^{12} = 2^{24}
\]

3. **Combine the results:**
So,
\[
-\frac{b^{12}}{4^{12}} = -\frac{b^{12}}{2^{24}}
\]

Now, let's consider the options given:
- \(-b^{1/3}\)
- \(-b^3\)
- \(-b^{-3}\)
- \(1/b^3\)

None of these options appear to match \(-\frac{b^{12}}{2^{24}}\) or simplify directly to that expression.

However, if you are specifically looking for a form in terms of \(b\) only and considering powers, note that \(-b^{-3}\) is equivalent to:
\[
-b^{-3} = -\frac{1}{b^3}
\]

While none of the listed options directly match \(-\left(\frac{b^1}{4}\right)^{12}\) exactly, if we reconsider any potential simplifications in interpretation of powers (or if additional context modifies the question), the choice \(-b^{-3}\) seems most aligned in a power-related form.

In conclusion, none of the given options directly simplify equivalently to the expression calculated, but if possibly selecting based on the form of power, **\(-b^{-3}\)** could be closest in context; otherwise, clarify the original intention of equivalency.