Solve 3^3/6+3^4/4+3^5/10

$$\frac { 3 ^ { 3 } } { 6 } + \frac { 3 ^ { 4 } } { 4 } + \frac { 3 ^ { 5 } } { 10 }$$

Evaluate

$$\frac{981}{20}=49.05$$

Solution Steps

Calculate 3 to the power of 3 and get 27.

$$\frac{27}{6}+\frac{3^{4}}{4}+\frac{3^{5}}{10}$$

Reduce the fraction \frac{27}{6} to lowest terms by extracting and canceling out 3.

$$\frac{9}{2}+\frac{3^{4}}{4}+\frac{3^{5}}{10}$$

Calculate 3 to the power of 4 and get 81.

$$\frac{9}{2}+\frac{81}{4}+\frac{3^{5}}{10}$$

Least common multiple of 2 and 4 is 4. Convert \frac{9}{2} and \frac{81}{4} to fractions with denominator 4.

$$\frac{18}{4}+\frac{81}{4}+\frac{3^{5}}{10}$$

Since \frac{18}{4} and \frac{81}{4} have the same denominator, add them by adding their numerators.

$$\frac{18+81}{4}+\frac{3^{5}}{10}$$

Add 18 and 81 to get 99.

$$\frac{99}{4}+\frac{3^{5}}{10}$$

Calculate 3 to the power of 5 and get 243.

$$\frac{99}{4}+\frac{243}{10}$$

Least common multiple of 4 and 10 is 20. Convert \frac{99}{4} and \frac{243}{10} to fractions with denominator 20.

$$\frac{495}{20}+\frac{486}{20}$$

Since \frac{495}{20} and \frac{486}{20} have the same denominator, add them by adding their numerators.

$$\frac{495+486}{20}$$

Add 495 and 486 to get 981.

$$\frac{981}{20}$$

Factor

$$\frac{3 ^ {2} \cdot 109}{2 ^ {2} \cdot 5} = 49\frac{1}{20} = 49.05$$