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-\frac{1}{8}\left(-\frac{1}{2}\right)^{0}-\left(-1\right)^{-5}
Calculate -2 to the power of -3 and get -\frac{1}{8}.
-\frac{1}{8}-\left(-1\right)^{-5}
Calculate -\frac{1}{2} to the power of 0 and get 1.
-\frac{1}{8}-\left(-1\right)
Calculate -1 to the power of -5 and get -1.
-\frac{1}{8}+1
The opposite of -1 is 1.
\frac{7}{8}
Add -\frac{1}{8} and 1 to get \frac{7}{8}.