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\left(1-2\right)^{-1}-\left(10^{-1}+\frac{1}{10}\right)
Calculate \sqrt[3]{-8} and get -2.
\left(-1\right)^{-1}-\left(10^{-1}+\frac{1}{10}\right)
Subtract 2 from 1 to get -1.
-1-\left(10^{-1}+\frac{1}{10}\right)
Calculate -1 to the power of -1 and get -1.
-1-\left(\frac{1}{10}+\frac{1}{10}\right)
Calculate 10 to the power of -1 and get \frac{1}{10}.
-1-\frac{1}{5}
Add \frac{1}{10} and \frac{1}{10} to get \frac{1}{5}.
-\frac{6}{5}
Subtract \frac{1}{5} from -1 to get -\frac{6}{5}.