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\left(-1\right)^{2021}+9^{0}
Multiply \left(\frac{2}{3}\right)^{-2} and \left(\frac{2}{3}\right)^{2} to get 1.
-1+9^{0}
Calculate -1 to the power of 2021 and get -1.
-1+1
Calculate 9 to the power of 0 and get 1.
0
Add -1 and 1 to get 0.