Solve 2+2^3/3!+2^5/5!

$$2 + \frac { 2 ^ { 3 } } { 3 ! } + \frac { 2 ^ { 5 } } { 5 ! }$$

Evaluate

$$\frac{18}{5}=3.6$$

Solution Steps

Calculate 2 to the power of 3 and get 8.

$$2+\frac{8}{3!}+\frac{2^{5}}{5!}$$

The factorial of 3 is 6.

$$2+\frac{8}{6}+\frac{2^{5}}{5!}$$

Reduce the fraction \frac{8}{6} to lowest terms by extracting and canceling out 2.

$$2+\frac{4}{3}+\frac{2^{5}}{5!}$$

Convert 2 to fraction \frac{6}{3}.

$$\frac{6}{3}+\frac{4}{3}+\frac{2^{5}}{5!}$$

Since \frac{6}{3} and \frac{4}{3} have the same denominator, add them by adding their numerators.

$$\frac{6+4}{3}+\frac{2^{5}}{5!}$$

Add 6 and 4 to get 10.

$$\frac{10}{3}+\frac{2^{5}}{5!}$$

Calculate 2 to the power of 5 and get 32.

$$\frac{10}{3}+\frac{32}{5!}$$

The factorial of 5 is 120.

$$\frac{10}{3}+\frac{32}{120}$$

Reduce the fraction \frac{32}{120} to lowest terms by extracting and canceling out 8.

$$\frac{10}{3}+\frac{4}{15}$$

Least common multiple of 3 and 15 is 15. Convert \frac{10}{3} and \frac{4}{15} to fractions with denominator 15.

$$\frac{50}{15}+\frac{4}{15}$$

Since \frac{50}{15} and \frac{4}{15} have the same denominator, add them by adding their numerators.

$$\frac{50+4}{15}$$

Add 50 and 4 to get 54.

$$\frac{54}{15}$$

Reduce the fraction \frac{54}{15} to lowest terms by extracting and canceling out 3.

$$\frac{18}{5}$$

Factor

$$\frac{2 \cdot 3 ^ {2}}{5} = 3\frac{3}{5} = 3.6$$