Solve frac{1}3^3-2*frac{1}3^2+1

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

Evaluate

$$\frac{22}{27}\approx 0.814814815$$

Solution Steps

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

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

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

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

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

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

Least common multiple of 27 and 9 is 27. Convert \frac{1}{27} and \frac{2}{9} to fractions with denominator 27.

$$\frac{1}{27}-\frac{6}{27}+1$$

Since \frac{1}{27} and \frac{6}{27} have the same denominator, subtract them by subtracting their numerators.

$$\frac{1-6}{27}+1$$

Subtract 6 from 1 to get -5.

$$-\frac{5}{27}+1$$

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

$$-\frac{5}{27}+\frac{27}{27}$$

Since -\frac{5}{27} and \frac{27}{27} have the same denominator, add them by adding their numerators.

$$\frac{-5+27}{27}$$

Add -5 and 27 to get 22.

$$\frac{22}{27}$$

Factor

$$\frac{2 \cdot 11}{3 ^ {3}} = 0.8148148148148148$$