Solve (1/8)^3-3/8+1/2

$$( \frac { 1 } { 8 } ) ^ { 3 } - \frac { 3 } { 8 } + \frac { 1 } { 2 }$$

Evaluate

$$\frac{65}{512}=0.126953125$$

Solution Steps

Calculate \frac{1}{8} to the power of 3 and get \frac{1}{512}.

$$\frac{1}{512}-\frac{3}{8}+\frac{1}{2}$$

Least common multiple of 512 and 8 is 512. Convert \frac{1}{512} and \frac{3}{8} to fractions with denominator 512.

$$\frac{1}{512}-\frac{192}{512}+\frac{1}{2}$$

Since \frac{1}{512} and \frac{192}{512} have the same denominator, subtract them by subtracting their numerators.

$$\frac{1-192}{512}+\frac{1}{2}$$

Subtract 192 from 1 to get -191.

$$-\frac{191}{512}+\frac{1}{2}$$

Least common multiple of 512 and 2 is 512. Convert -\frac{191}{512} and \frac{1}{2} to fractions with denominator 512.

$$-\frac{191}{512}+\frac{256}{512}$$

Since -\frac{191}{512} and \frac{256}{512} have the same denominator, add them by adding their numerators.

$$\frac{-191+256}{512}$$

Add -191 and 256 to get 65.

$$\frac{65}{512}$$

Factor

$$\frac{5 \cdot 13}{2 ^ {9}} = 0.126953125$$