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-\left(-\frac{1}{2}+\frac{1}{6}\right)^{4}
The opposite of -\frac{1}{6} is \frac{1}{6}.
-\left(-\frac{1}{3}\right)^{4}
Add -\frac{1}{2} and \frac{1}{6} to get -\frac{1}{3}.
-\frac{1}{81}
Calculate -\frac{1}{3} to the power of 4 and get \frac{1}{81}.