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-\frac{1}{2}-\left(\log_{4}\left(\frac{1}{16}\right)\right)^{3}
The base 4 logarithm of \frac{1}{2} is -\frac{1}{2}.
-\frac{1}{2}-\left(-2\right)^{3}
The base 4 logarithm of \frac{1}{16} is -2.
-\frac{1}{2}-\left(-8\right)
Calculate -2 to the power of 3 and get -8.
-\frac{1}{2}+8
The opposite of -8 is 8.
\frac{15}{2}
Add -\frac{1}{2} and 8 to get \frac{15}{2}.