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1+\frac{5^{2}}{25^{0}}-5^{1}
Calculate 1 to the power of 5 and get 1.
1+\frac{25}{25^{0}}-5^{1}
Calculate 5 to the power of 2 and get 25.
1+\frac{25}{1}-5^{1}
Calculate 25 to the power of 0 and get 1.
1+25-5^{1}
Anything divided by one gives itself.
26-5^{1}
Add 1 and 25 to get 26.
26-5
Calculate 5 to the power of 1 and get 5.
21
Subtract 5 from 26 to get 21.