Solve 2/3+(3/7)^2+(4/11)^3+(5/15)^4

$$\frac { 2 } { 3 } + ( \frac { 3 } { 7 } ) ^ { 2 } + ( \frac { 4 } { 11 } ) ^ { 3 } + ( \frac { 5 } { 15 } ) ^ { 4 }$$

Evaluate

$$\frac{4811360}{5282739}\approx 0.910769962$$

Solution Steps

Calculate \frac{3}{7} to the power of 2 and get \frac{9}{49}.

$$\frac{2}{3}+\frac{9}{49}+\left(\frac{4}{11}\right)^{3}+\left(\frac{5}{15}\right)^{4}$$

Add \frac{2}{3} and \frac{9}{49} to get \frac{125}{147}.

$$\frac{125}{147}+\left(\frac{4}{11}\right)^{3}+\left(\frac{5}{15}\right)^{4}$$

Calculate \frac{4}{11} to the power of 3 and get \frac{64}{1331}.

$$\frac{125}{147}+\frac{64}{1331}+\left(\frac{5}{15}\right)^{4}$$

Add \frac{125}{147} and \frac{64}{1331} to get \frac{175783}{195657}.

$$\frac{175783}{195657}+\left(\frac{5}{15}\right)^{4}$$

Reduce the fraction \frac{5}{15} to lowest terms by extracting and canceling out 5.

$$\frac{175783}{195657}+\left(\frac{1}{3}\right)^{4}$$

Calculate \frac{1}{3} to the power of 4 and get \frac{1}{81}.

$$\frac{175783}{195657}+\frac{1}{81}$$

Add \frac{175783}{195657} and \frac{1}{81} to get \frac{4811360}{5282739}.

$$\frac{4811360}{5282739}$$

Factor

$$\frac{2 ^ {5} \cdot 5 \cdot 30071}{3 ^ {4} \cdot 7 ^ {2} \cdot 11 ^ {3}} = 0.9107699623244684$$