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2-\left(\sqrt{3}\right)^{0}+\left(-1\right)^{2019}
The absolute value of a real number a is a when a\geq 0, or -a when a<0. The absolute value of -2 is 2.
2-1+\left(-1\right)^{2019}
Calculate \sqrt{3} to the power of 0 and get 1.
1+\left(-1\right)^{2019}
Subtract 1 from 2 to get 1.
1-1
Calculate -1 to the power of 2019 and get -1.
0
Subtract 1 from 1 to get 0.