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1+\left(-1\right)^{2018}-\frac{1}{2}
Calculate -2 to the power of 0 and get 1.
1+1-\frac{1}{2}
Calculate -1 to the power of 2018 and get 1.
2-\frac{1}{2}
Add 1 and 1 to get 2.
\frac{3}{2}
Subtract \frac{1}{2} from 2 to get \frac{3}{2}.