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\sqrt{1\times 1^{2^{2}}}
Divide x by x to get 1.
\sqrt{1\times 1^{4}}
Calculate 2 to the power of 2 and get 4.
\sqrt{1\times 1}
Calculate 1 to the power of 4 and get 1.
\sqrt{1}
Multiply 1 and 1 to get 1.
1
Calculate the square root of 1 and get 1.