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1^{5-|-4\times 2|}
Add -6 and 11 to get 5.
1^{5-|-8|}
Multiply -4 and 2 to get -8.
1^{5-8}
The absolute value of a real number a is a when a\geq 0, or -a when a<0. The absolute value of -8 is 8.
1^{-3}
Subtract 8 from 5 to get -3.
1
Calculate 1 to the power of -3 and get 1.