Solve (2/3)^3+(5/20-3/9)^9

$$( \frac { 2 } { 3 } ) ^ { 3 } + ( \frac { 5 } { 20 } - \frac { 3 } { 9 } ) ^ { 9 }$$

Evaluate

$$\frac{1528823807}{5159780352}\approx 0.296296296$$

Solution Steps

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

$$\frac{8}{27}+\left(\frac{5}{20}-\frac{3}{9}\right)^{9}$$

Reduce the fraction \frac{5}{20} to lowest terms by extracting and canceling out 5.

$$\frac{8}{27}+\left(\frac{1}{4}-\frac{3}{9}\right)^{9}$$

Reduce the fraction \frac{3}{9} to lowest terms by extracting and canceling out 3.

$$\frac{8}{27}+\left(\frac{1}{4}-\frac{1}{3}\right)^{9}$$

Subtract \frac{1}{3} from \frac{1}{4} to get -\frac{1}{12}.

$$\frac{8}{27}+\left(-\frac{1}{12}\right)^{9}$$

Calculate -\frac{1}{12} to the power of 9 and get -\frac{1}{5159780352}.

$$\frac{8}{27}-\frac{1}{5159780352}$$

Subtract \frac{1}{5159780352} from \frac{8}{27} to get \frac{1528823807}{5159780352}.

$$\frac{1528823807}{5159780352}$$

Factor

$$\frac{7 \cdot 31 \cdot 1151 \cdot 6121}{2 ^ {18} \cdot 3 ^ {9}} = 0.2962962961024896$$