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2-3^{-2}-3^{0}
Calculate the square root of 4 and get 2.
2-\frac{1}{9}-3^{0}
Calculate 3 to the power of -2 and get \frac{1}{9}.
\frac{17}{9}-3^{0}
Subtract \frac{1}{9} from 2 to get \frac{17}{9}.
\frac{17}{9}-1
Calculate 3 to the power of 0 and get 1.
\frac{8}{9}
Subtract 1 from \frac{17}{9} to get \frac{8}{9}.