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16-\left(-5\right)^{2}+\left(-1\right)^{8}
The square of \sqrt{16} is 16.
16-25+\left(-1\right)^{8}
Calculate -5 to the power of 2 and get 25.
-9+\left(-1\right)^{8}
Subtract 25 from 16 to get -9.
-9+1
Calculate -1 to the power of 8 and get 1.
-8
Add -9 and 1 to get -8.