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-4+\sqrt{\left(-2\right)^{2}}-\sqrt[3]{-8^{2}}
Calculate -2 to the power of 2 and get 4.
-4+\sqrt{4}-\sqrt[3]{-8^{2}}
Calculate -2 to the power of 2 and get 4.
-4+2-\sqrt[3]{-8^{2}}
Calculate the square root of 4 and get 2.
-2-\sqrt[3]{-8^{2}}
Add -4 and 2 to get -2.
-2-\sqrt[3]{-64}
Calculate 8 to the power of 2 and get 64.
-2-\left(-4\right)
Calculate \sqrt[3]{-64} and get -4.
-2+4
The opposite of -4 is 4.
2
Add -2 and 4 to get 2.