Solve 3^{-2}-3^-1+3^0-3^1+3^2

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

Evaluate

$$\frac{61}{9}\approx 6.777777778$$

Solution Steps

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

$$\frac{1}{9}-3^{-1}+3^{0}-3^{1}+3^{2}$$

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

$$\frac{1}{9}-\frac{1}{3}+3^{0}-3^{1}+3^{2}$$

Subtract \frac{1}{3} from \frac{1}{9} to get -\frac{2}{9}.

$$-\frac{2}{9}+3^{0}-3^{1}+3^{2}$$

Calculate 3 to the power of 0 and get 1.

$$-\frac{2}{9}+1-3^{1}+3^{2}$$

Add -\frac{2}{9} and 1 to get \frac{7}{9}.

$$\frac{7}{9}-3^{1}+3^{2}$$

Calculate 3 to the power of 1 and get 3.

$$\frac{7}{9}-3+3^{2}$$

Subtract 3 from \frac{7}{9} to get -\frac{20}{9}.

$$-\frac{20}{9}+3^{2}$$

Calculate 3 to the power of 2 and get 9.

$$-\frac{20}{9}+9$$

Add -\frac{20}{9} and 9 to get \frac{61}{9}.

$$\frac{61}{9}$$

Factor

$$\frac{61}{3 ^ {2}} = 6\frac{7}{9} = 6.777777777777778$$