Solve {left(1/2right)}^6+{left(5/2right)}^2

$${ \left( \frac{ 1 }{ 2 } \right) }^{ 6 } + { \left( \frac{ 5 }{ 2 } \right) }^{ 2 }$$

Evaluate

$$\frac{401}{64}=6.265625$$

Solution Steps

Calculate \frac{1}{2} to the power of 6 and get \frac{1}{64}.

$$\frac{1}{64}+\left(\frac{5}{2}\right)^{2}$$

Calculate \frac{5}{2} to the power of 2 and get \frac{25}{4}.

$$\frac{1}{64}+\frac{25}{4}$$

Least common multiple of 64 and 4 is 64. Convert \frac{1}{64} and \frac{25}{4} to fractions with denominator 64.

$$\frac{1}{64}+\frac{400}{64}$$

Since \frac{1}{64} and \frac{400}{64} have the same denominator, add them by adding their numerators.

$$\frac{1+400}{64}$$

Add 1 and 400 to get 401.

$$\frac{401}{64}$$

Factor

$$\frac{401}{2 ^ {6}} = 6\frac{17}{64} = 6.265625$$