Solve 1/2-3(1/2)^2+6(1/2)^3

$$\frac { 1 } { 2 } - 3 ( \frac { 1 } { 2 } ) ^ { 2 } + 6 ( \frac { 1 } { 2 } ) ^ { 3 }$$

Evaluate

$$\frac{1}{2}=0.5$$

Solution Steps

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

$$\frac{1}{2}-3\times \frac{1}{4}+6\times \left(\frac{1}{2}\right)^{3}$$

Multiply 3 and \frac{1}{4} to get \frac{3}{4}.

$$\frac{1}{2}-\frac{3}{4}+6\times \left(\frac{1}{2}\right)^{3}$$

Least common multiple of 2 and 4 is 4. Convert \frac{1}{2} and \frac{3}{4} to fractions with denominator 4.

$$\frac{2}{4}-\frac{3}{4}+6\times \left(\frac{1}{2}\right)^{3}$$

Since \frac{2}{4} and \frac{3}{4} have the same denominator, subtract them by subtracting their numerators.

$$\frac{2-3}{4}+6\times \left(\frac{1}{2}\right)^{3}$$

Subtract 3 from 2 to get -1.

$$-\frac{1}{4}+6\times \left(\frac{1}{2}\right)^{3}$$

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

$$-\frac{1}{4}+6\times \frac{1}{8}$$

Multiply 6 and \frac{1}{8} to get \frac{6}{8}.

$$-\frac{1}{4}+\frac{6}{8}$$

Reduce the fraction \frac{6}{8} to lowest terms by extracting and canceling out 2.

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

Since -\frac{1}{4} and \frac{3}{4} have the same denominator, add them by adding their numerators.

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

Add -1 and 3 to get 2.

$$\frac{2}{4}$$

Reduce the fraction \frac{2}{4} to lowest terms by extracting and canceling out 2.

$$\frac{1}{2}$$

Factor

$$\frac{1}{2} = 0.5$$