Solve 3(1/3)^3-2(1/3)^2+(1/3)

$$3 ( \frac { 1 } { 3 } ) ^ { 3 } - 2 ( \frac { 1 } { 3 } ) ^ { 2 } + ( \frac { 1 } { 3 } )$$

Evaluate

$$\frac{2}{9}\approx 0.222222222$$

Solution Steps

Calculate \frac{1}{3} to the power of 3 and get \frac{1}{27}.

$$3\times \frac{1}{27}-2\times \left(\frac{1}{3}\right)^{2}+\frac{1}{3}$$

Multiply 3 and \frac{1}{27} to get \frac{3}{27}.

$$\frac{3}{27}-2\times \left(\frac{1}{3}\right)^{2}+\frac{1}{3}$$

Reduce the fraction \frac{3}{27} to lowest terms by extracting and canceling out 3.

$$\frac{1}{9}-2\times \left(\frac{1}{3}\right)^{2}+\frac{1}{3}$$

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

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

Multiply 2 and \frac{1}{9} to get \frac{2}{9}.

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

Since \frac{1}{9} and \frac{2}{9} have the same denominator, subtract them by subtracting their numerators.

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

Subtract 2 from 1 to get -1.

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

Least common multiple of 9 and 3 is 9. Convert -\frac{1}{9} and \frac{1}{3} to fractions with denominator 9.

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

Since -\frac{1}{9} and \frac{3}{9} have the same denominator, add them by adding their numerators.

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

Add -1 and 3 to get 2.

$$\frac{2}{9}$$

Factor

$$\frac{2}{3 ^ {2}} = 0.2222222222222222$$