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2-\sqrt[4]{16}+\sqrt[8]{1}
Calculate \sqrt[3]{8} and get 2.
2-2+\sqrt[8]{1}
Calculate \sqrt[4]{16} and get 2.
0+\sqrt[8]{1}
Subtract 2 from 2 to get 0.
0+1
Calculate \sqrt[8]{1} and get 1.
1
Add 0 and 1 to get 1.