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A=5+\left(2012+\sqrt{2013}\right)^{0}+81^{\frac{1}{4}}
Calculate \frac{1}{5} to the power of -1 and get 5.
A=5+1+81^{\frac{1}{4}}
Calculate 2012+\sqrt{2013} to the power of 0 and get 1.
A=6+81^{\frac{1}{4}}
Add 5 and 1 to get 6.
A=6+3
Calculate 81 to the power of \frac{1}{4} and get 3.
A=9
Add 6 and 3 to get 9.