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

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

Evaluate

$$\frac{16}{27}\approx 0.592592593$$

Solution Steps

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

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

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

$$\frac{1}{27}-\frac{1}{9}-\frac{1}{3}+1$$

Least common multiple of 27 and 9 is 27. Convert \frac{1}{27} and \frac{1}{9} to fractions with denominator 27.

$$\frac{1}{27}-\frac{3}{27}-\frac{1}{3}+1$$

Since \frac{1}{27} and \frac{3}{27} have the same denominator, subtract them by subtracting their numerators.

$$\frac{1-3}{27}-\frac{1}{3}+1$$

Subtract 3 from 1 to get -2.

$$-\frac{2}{27}-\frac{1}{3}+1$$

Least common multiple of 27 and 3 is 27. Convert -\frac{2}{27} and \frac{1}{3} to fractions with denominator 27.

$$-\frac{2}{27}-\frac{9}{27}+1$$

Since -\frac{2}{27} and \frac{9}{27} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-2-9}{27}+1$$

Subtract 9 from -2 to get -11.

$$-\frac{11}{27}+1$$

Convert 1 to fraction \frac{27}{27}.

$$-\frac{11}{27}+\frac{27}{27}$$

Since -\frac{11}{27} and \frac{27}{27} have the same denominator, add them by adding their numerators.

$$\frac{-11+27}{27}$$

Add -11 and 27 to get 16.

$$\frac{16}{27}$$

Factor

$$\frac{2 ^ {4}}{3 ^ {3}} = 0.5925925925925926$$