Solve {left(3/2right)}^2+{left(1/2right)}^3

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

Evaluate

$$\frac{19}{8}=2.375$$

Solution Steps

Calculate \frac{3}{2} to the power of 2 and get \frac{9}{4}.

$$\frac{9}{4}+\left(\frac{1}{2}\right)^{3}$$

Calculate \frac{1}{2} to the power of 3 and get \frac{1}{8}.

$$\frac{9}{4}+\frac{1}{8}$$

Least common multiple of 4 and 8 is 8. Convert \frac{9}{4} and \frac{1}{8} to fractions with denominator 8.

$$\frac{18}{8}+\frac{1}{8}$$

Since \frac{18}{8} and \frac{1}{8} have the same denominator, add them by adding their numerators.

$$\frac{18+1}{8}$$

Add 18 and 1 to get 19.

$$\frac{19}{8}$$

Factor

$$\frac{19}{2 ^ {3}} = 2\frac{3}{8} = 2.375$$