Solve 7/2^4-5/2^3+3/2^2-1/2=

$$\frac { 7 } { 2 ^ { 4 } } - \frac { 5 } { 2 ^ { 3 } } + \frac { 3 } { 2 ^ { 2 } } - \frac { 1 } { 2 } =$$

Evaluate

$$\frac{1}{16}=0.0625$$

Solution Steps

Calculate 2 to the power of 4 and get 16.

$$\frac{7}{16}-\frac{5}{2^{3}}+\frac{3}{2^{2}}-\frac{1}{2}$$

Calculate 2 to the power of 3 and get 8.

$$\frac{7}{16}-\frac{5}{8}+\frac{3}{2^{2}}-\frac{1}{2}$$

Least common multiple of 16 and 8 is 16. Convert \frac{7}{16} and \frac{5}{8} to fractions with denominator 16.

$$\frac{7}{16}-\frac{10}{16}+\frac{3}{2^{2}}-\frac{1}{2}$$

Since \frac{7}{16} and \frac{10}{16} have the same denominator, subtract them by subtracting their numerators.

$$\frac{7-10}{16}+\frac{3}{2^{2}}-\frac{1}{2}$$

Subtract 10 from 7 to get -3.

$$-\frac{3}{16}+\frac{3}{2^{2}}-\frac{1}{2}$$

Calculate 2 to the power of 2 and get 4.

$$-\frac{3}{16}+\frac{3}{4}-\frac{1}{2}$$

Least common multiple of 16 and 4 is 16. Convert -\frac{3}{16} and \frac{3}{4} to fractions with denominator 16.

$$-\frac{3}{16}+\frac{12}{16}-\frac{1}{2}$$

Since -\frac{3}{16} and \frac{12}{16} have the same denominator, add them by adding their numerators.

$$\frac{-3+12}{16}-\frac{1}{2}$$

Add -3 and 12 to get 9.

$$\frac{9}{16}-\frac{1}{2}$$

Least common multiple of 16 and 2 is 16. Convert \frac{9}{16} and \frac{1}{2} to fractions with denominator 16.

$$\frac{9}{16}-\frac{8}{16}$$

Since \frac{9}{16} and \frac{8}{16} have the same denominator, subtract them by subtracting their numerators.

$$\frac{9-8}{16}$$

Subtract 8 from 9 to get 1.

$$\frac{1}{16}$$

Factor

$$\frac{1}{2 ^ {4}} = 0.0625$$