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

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

Evaluate

$$\frac{69}{8}=8.625$$

Solution Steps

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

$$\frac{1}{8}+2\times \left(\frac{1}{2}\right)^{2}+8$$

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

$$\frac{1}{8}+2\times \frac{1}{4}+8$$

Multiply 2 and \frac{1}{4} to get \frac{2}{4}.

$$\frac{1}{8}+\frac{2}{4}+8$$

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

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

Least common multiple of 8 and 2 is 8. Convert \frac{1}{8} and \frac{1}{2} to fractions with denominator 8.

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

Since \frac{1}{8} and \frac{4}{8} have the same denominator, add them by adding their numerators.

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

Add 1 and 4 to get 5.

$$\frac{5}{8}+8$$

Convert 8 to fraction \frac{64}{8}.

$$\frac{5}{8}+\frac{64}{8}$$

Since \frac{5}{8} and \frac{64}{8} have the same denominator, add them by adding their numerators.

$$\frac{5+64}{8}$$

Add 5 and 64 to get 69.

$$\frac{69}{8}$$

Factor

$$\frac{3 \cdot 23}{2 ^ {3}} = 8\frac{5}{8} = 8.625$$