Solve 1/27*2/3+1/3*(2/3)^3+(frac{1}{3})^4+(frac{2}{3})^4

$$\frac { 1 } { 27 } \times \frac { 2 } { 3 } + \frac { 1 } { 3 } \times ( \frac { 2 } { 3 } ) ^ { 3 } + ( \frac { 1 } { 3 } ) ^ { 4 } + ( \frac { 2 } { 3 } ) ^ { 4 }$$

Evaluate

$$\frac{1}{3}\approx 0.333333333$$

Solution Steps

Multiply \frac{1}{27} times \frac{2}{3} by multiplying numerator times numerator and denominator times denominator.

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

Do the multiplications in the fraction \frac{1\times 2}{27\times 3}.

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

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

$$\frac{2}{81}+\frac{1}{3}\times \frac{8}{27}+\left(\frac{1}{3}\right)^{4}+\left(\frac{2}{3}\right)^{4}$$

Multiply \frac{1}{3} times \frac{8}{27} by multiplying numerator times numerator and denominator times denominator.

$$\frac{2}{81}+\frac{1\times 8}{3\times 27}+\left(\frac{1}{3}\right)^{4}+\left(\frac{2}{3}\right)^{4}$$

Do the multiplications in the fraction \frac{1\times 8}{3\times 27}.

$$\frac{2}{81}+\frac{8}{81}+\left(\frac{1}{3}\right)^{4}+\left(\frac{2}{3}\right)^{4}$$

Since \frac{2}{81} and \frac{8}{81} have the same denominator, add them by adding their numerators.

$$\frac{2+8}{81}+\left(\frac{1}{3}\right)^{4}+\left(\frac{2}{3}\right)^{4}$$

Add 2 and 8 to get 10.

$$\frac{10}{81}+\left(\frac{1}{3}\right)^{4}+\left(\frac{2}{3}\right)^{4}$$

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

$$\frac{10}{81}+\frac{1}{81}+\left(\frac{2}{3}\right)^{4}$$

Since \frac{10}{81} and \frac{1}{81} have the same denominator, add them by adding their numerators.

$$\frac{10+1}{81}+\left(\frac{2}{3}\right)^{4}$$

Add 10 and 1 to get 11.

$$\frac{11}{81}+\left(\frac{2}{3}\right)^{4}$$

Calculate \frac{2}{3} to the power of 4 and get \frac{16}{81}.

$$\frac{11}{81}+\frac{16}{81}$$

Since \frac{11}{81} and \frac{16}{81} have the same denominator, add them by adding their numerators.

$$\frac{11+16}{81}$$

Add 11 and 16 to get 27.

$$\frac{27}{81}$$

Reduce the fraction \frac{27}{81} to lowest terms by extracting and canceling out 27.

$$\frac{1}{3}$$

Factor

$$\frac{1}{3} = 0.3333333333333333$$