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\frac{1}{9}+\left(-2\right)^{0}-|-4|
Calculate 3 to the power of -2 and get \frac{1}{9}.
\frac{1}{9}+1-|-4|
Calculate -2 to the power of 0 and get 1.
\frac{10}{9}-|-4|
Add \frac{1}{9} and 1 to get \frac{10}{9}.
\frac{10}{9}-4
The absolute value of a real number a is a when a\geq 0, or -a when a<0. The absolute value of -4 is 4.
-\frac{26}{9}
Subtract 4 from \frac{10}{9} to get -\frac{26}{9}.