Solve [(1/2)^{0}+1/2+(1/2)^{2}+(1/2)^3]:(2^0+2+2^2+2^3)=

$$[ ( \frac { 1 } { 2 } ) ^ { 0 } + \frac { 1 } { 2 } + ( \frac { 1 } { 2 } ) ^ { 2 } + ( \frac { 1 } { 2 } ) ^ { 3 } ] : ( 2 ^ { 0 } + 2 + 2 ^ { 2 } + 2 ^ { 3 } ) =$$

Evaluate

$$\frac{1}{8}=0.125$$

Solution Steps

Calculate \frac{1}{2} to the power of 0 and get 1.

$$\frac{1+\frac{1}{2}+\left(\frac{1}{2}\right)^{2}+\left(\frac{1}{2}\right)^{3}}{2^{0}+2+2^{2}+2^{3}}$$

Add 1 and \frac{1}{2} to get \frac{3}{2}.

$$\frac{\frac{3}{2}+\left(\frac{1}{2}\right)^{2}+\left(\frac{1}{2}\right)^{3}}{2^{0}+2+2^{2}+2^{3}}$$

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

$$\frac{\frac{3}{2}+\frac{1}{4}+\left(\frac{1}{2}\right)^{3}}{2^{0}+2+2^{2}+2^{3}}$$

Add \frac{3}{2} and \frac{1}{4} to get \frac{7}{4}.

$$\frac{\frac{7}{4}+\left(\frac{1}{2}\right)^{3}}{2^{0}+2+2^{2}+2^{3}}$$

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

$$\frac{\frac{7}{4}+\frac{1}{8}}{2^{0}+2+2^{2}+2^{3}}$$

Add \frac{7}{4} and \frac{1}{8} to get \frac{15}{8}.

$$\frac{\frac{15}{8}}{2^{0}+2+2^{2}+2^{3}}$$

Calculate 2 to the power of 0 and get 1.

$$\frac{\frac{15}{8}}{1+2+2^{2}+2^{3}}$$

Add 1 and 2 to get 3.

$$\frac{\frac{15}{8}}{3+2^{2}+2^{3}}$$

Calculate 2 to the power of 2 and get 4.

$$\frac{\frac{15}{8}}{3+4+2^{3}}$$

Add 3 and 4 to get 7.

$$\frac{\frac{15}{8}}{7+2^{3}}$$

Calculate 2 to the power of 3 and get 8.

$$\frac{\frac{15}{8}}{7+8}$$

Add 7 and 8 to get 15.

$$\frac{\frac{15}{8}}{15}$$

Express \frac{\frac{15}{8}}{15} as a single fraction.

$$\frac{15}{8\times 15}$$

Cancel out 15 in both numerator and denominator.

$$\frac{1}{8}$$

Factor

$$\frac{1}{2 ^ {3}} = 0.125$$