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1-2+16^{\frac{1}{4}}-\left(-2\right)^{2}+27^{\frac{1}{3}}
Calculate \sqrt[3]{8} and get 2.
-1+16^{\frac{1}{4}}-\left(-2\right)^{2}+27^{\frac{1}{3}}
Subtract 2 from 1 to get -1.
-1+2-\left(-2\right)^{2}+27^{\frac{1}{3}}
Calculate 16 to the power of \frac{1}{4} and get 2.
1-\left(-2\right)^{2}+27^{\frac{1}{3}}
Add -1 and 2 to get 1.
1-4+27^{\frac{1}{3}}
Calculate -2 to the power of 2 and get 4.
-3+27^{\frac{1}{3}}
Subtract 4 from 1 to get -3.
-3+3
Calculate 27 to the power of \frac{1}{3} and get 3.
0
Add -3 and 3 to get 0.