Solve 27*frac{1}3^5-2*frac{1}3^3+1/3=

$$27 \cdot \frac { 1 } { 3 } ^ { 5 } - 2 \cdot \frac { 1 } { 3 } ^ { 3 } + \frac { 1 } { 3 } =$$

Evaluate

$$\frac{10}{27}\approx 0.37037037$$

Solution Steps

Calculate \frac{1}{3} to the power of 5 and get \frac{1}{243}.

$$27\times \frac{1}{243}-2\times \left(\frac{1}{3}\right)^{3}+\frac{1}{3}$$

Multiply 27 and \frac{1}{243} to get \frac{27}{243}.

$$\frac{27}{243}-2\times \left(\frac{1}{3}\right)^{3}+\frac{1}{3}$$

Reduce the fraction \frac{27}{243} to lowest terms by extracting and canceling out 27.

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

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

$$\frac{1}{9}-2\times \frac{1}{27}+\frac{1}{3}$$

Multiply 2 and \frac{1}{27} to get \frac{2}{27}.

$$\frac{1}{9}-\frac{2}{27}+\frac{1}{3}$$

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

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

Since \frac{3}{27} and \frac{2}{27} have the same denominator, subtract them by subtracting their numerators.

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

Subtract 2 from 3 to get 1.

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

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

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

Since \frac{1}{27} and \frac{9}{27} have the same denominator, add them by adding their numerators.

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

Add 1 and 9 to get 10.

$$\frac{10}{27}$$

Factor

$$\frac{2 \cdot 5}{3 ^ {3}} = 0.37037037037037035$$