Solve (1/2)^4-1/2+2

$$( \frac { 1 } { 2 } ) ^ { 4 } - \frac { 1 } { 2 } + 2$$

Evaluate

$$\frac{25}{16}=1.5625$$

Solution Steps

Calculate \frac{1}{2} to the power of 4 and get \frac{1}{16}.

$$\frac{1}{16}-\frac{1}{2}+2$$

Least common multiple of 16 and 2 is 16. Convert \frac{1}{16} and \frac{1}{2} to fractions with denominator 16.

$$\frac{1}{16}-\frac{8}{16}+2$$

Since \frac{1}{16} and \frac{8}{16} have the same denominator, subtract them by subtracting their numerators.

$$\frac{1-8}{16}+2$$

Subtract 8 from 1 to get -7.

$$-\frac{7}{16}+2$$

Convert 2 to fraction \frac{32}{16}.

$$-\frac{7}{16}+\frac{32}{16}$$

Since -\frac{7}{16} and \frac{32}{16} have the same denominator, add them by adding their numerators.

$$\frac{-7+32}{16}$$

Add -7 and 32 to get 25.

$$\frac{25}{16}$$

Factor

$$\frac{5 ^ {2}}{2 ^ {4}} = 1\frac{9}{16} = 1.5625$$