Solve 3^0-3^-2+4^-1+5^-5

$$3 ^ { 0 } - 3 ^ { - 2 } + 4 ^ { - 1 } + 5 ^ { - 5 }$$

Evaluate

$$\frac{128161}{112500}\approx 1.139208889$$

Solution Steps

Calculate 3 to the power of 0 and get 1.

$$1-3^{-2}+4^{-1}+5^{-5}$$

Calculate 3 to the power of -2 and get \frac{1}{9}.

$$1-\frac{1}{9}+4^{-1}+5^{-5}$$

Subtract \frac{1}{9} from 1 to get \frac{8}{9}.

$$\frac{8}{9}+4^{-1}+5^{-5}$$

Calculate 4 to the power of -1 and get \frac{1}{4}.

$$\frac{8}{9}+\frac{1}{4}+5^{-5}$$

Add \frac{8}{9} and \frac{1}{4} to get \frac{41}{36}.

$$\frac{41}{36}+5^{-5}$$

Calculate 5 to the power of -5 and get \frac{1}{3125}.

$$\frac{41}{36}+\frac{1}{3125}$$

Add \frac{41}{36} and \frac{1}{3125} to get \frac{128161}{112500}.

$$\frac{128161}{112500}$$

Factor

$$\frac{11 \cdot 61 \cdot 191}{2 ^ {2} \cdot 3 ^ {2} \cdot 5 ^ {5}} = 1\frac{15661}{112500} = 1.139208888888889$$