To simplify the expression \(-\left(\frac{b^1}{4}\right)^{12}\):
-
Apply the exponent: When raising a fraction to an exponent, you can apply the exponent to both the numerator and the denominator: \[ -\left(\frac{b^1}{4}\right)^{12} = -\frac{(b^1)^{12}}{4^{12}} = -\frac{b^{12}}{4^{12}} \]
-
Rewrite \(4^{12}\): \[ 4^{12} = (2^2)^{12} = 2^{24} \]
-
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.