To find an equivalent expression for \(-\left(\frac{b}{4}\right)^{12}\), we can break it down as follows:
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The expression \(\left(\frac{b}{4}\right)^{12}\) can be rewritten using the property of exponents:
\[ \left(\frac{b}{4}\right)^{12} = \frac{b^{12}}{4^{12}} \]
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Next, we substitute this into the expression:
\[ -\left(\frac{b}{4}\right)^{12} = -\frac{b^{12}}{4^{12}} \]
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Finally, \(4^{12}\) can be calculated if desired, but it can also be left in exponential form. The expression for \(4^{12}\) is \( (2^2)^{12} = 2^{24} \), but this simplifies the expression only when needed.
Thus, the equivalent expression for \(-\left(\frac{b}{4}\right)^{12}\) is:
\[ -\frac{b^{12}}{4^{12}} \text{ or } -\frac{b^{12}}{2^{24}} \]
Either form is equally valid, so you can use the one that best fits your needs.