Solve {left(2/3right)}^3-{left(2/3right)}^2+2/3

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

Evaluate

$$\frac{14}{27}\approx 0.518518519$$

Solution Steps

Calculate \frac{2}{3} to the power of 3 and get \frac{8}{27}.

$$\frac{8}{27}-\left(\frac{2}{3}\right)^{2}+\frac{2}{3}$$

Calculate \frac{2}{3} to the power of 2 and get \frac{4}{9}.

$$\frac{8}{27}-\frac{4}{9}+\frac{2}{3}$$

Least common multiple of 27 and 9 is 27. Convert \frac{8}{27} and \frac{4}{9} to fractions with denominator 27.

$$\frac{8}{27}-\frac{12}{27}+\frac{2}{3}$$

Since \frac{8}{27} and \frac{12}{27} have the same denominator, subtract them by subtracting their numerators.

$$\frac{8-12}{27}+\frac{2}{3}$$

Subtract 12 from 8 to get -4.

$$-\frac{4}{27}+\frac{2}{3}$$

Least common multiple of 27 and 3 is 27. Convert -\frac{4}{27} and \frac{2}{3} to fractions with denominator 27.

$$-\frac{4}{27}+\frac{18}{27}$$

Since -\frac{4}{27} and \frac{18}{27} have the same denominator, add them by adding their numerators.

$$\frac{-4+18}{27}$$

Add -4 and 18 to get 14.

$$\frac{14}{27}$$

Factor

$$\frac{2 \cdot 7}{3 ^ {3}} = 0.5185185185185185$$