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