Solve [(1/3-1/9)^2+(1/3)^3]*3^2/7

$$[ ( \frac { 1 } { 3 } - \frac { 1 } { 9 } ) ^ { 2 } + ( \frac { 1 } { 3 } ) ^ { 3 } ] \times \frac { 3 ^ { 2 } } { 7 }$$

Evaluate

$$\frac{1}{9}\approx 0.111111111$$

Solution Steps

Subtract \frac{1}{9} from \frac{1}{3} to get \frac{2}{9}.

$$\left(\left(\frac{2}{9}\right)^{2}+\left(\frac{1}{3}\right)^{3}\right)\times \frac{3^{2}}{7}$$

Calculate \frac{2}{9} to the power of 2 and get \frac{4}{81}.

$$\left(\frac{4}{81}+\left(\frac{1}{3}\right)^{3}\right)\times \frac{3^{2}}{7}$$

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

$$\left(\frac{4}{81}+\frac{1}{27}\right)\times \frac{3^{2}}{7}$$

Add \frac{4}{81} and \frac{1}{27} to get \frac{7}{81}.

$$\frac{7}{81}\times \frac{3^{2}}{7}$$

Calculate 3 to the power of 2 and get 9.

$$\frac{7}{81}\times \frac{9}{7}$$

Multiply \frac{7}{81} and \frac{9}{7} to get \frac{1}{9}.

$$\frac{1}{9}$$

Factor

$$\frac{1}{3 ^ {2}} = 0.1111111111111111$$