Solve 1-(-1/2)^4/1-(-frac{1{2})}

$$\frac { 1 - ( - \frac { 1 } { 2 } ) ^ { 4 } } { 1 - ( - \frac { 1 } { 2 } ) }$$

Evaluate

$$\frac{5}{8}=0.625$$

Solution Steps

Calculate -\frac{1}{2} to the power of 4 and get \frac{1}{16}.

$$\frac{1-\frac{1}{16}}{1-\left(-\frac{1}{2}\right)}$$

Convert 1 to fraction \frac{16}{16}.

$$\frac{\frac{16}{16}-\frac{1}{16}}{1-\left(-\frac{1}{2}\right)}$$

Since \frac{16}{16} and \frac{1}{16} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{16-1}{16}}{1-\left(-\frac{1}{2}\right)}$$

Subtract 1 from 16 to get 15.

$$\frac{\frac{15}{16}}{1-\left(-\frac{1}{2}\right)}$$

The opposite of -\frac{1}{2} is \frac{1}{2}.

$$\frac{\frac{15}{16}}{1+\frac{1}{2}}$$

Convert 1 to fraction \frac{2}{2}.

$$\frac{\frac{15}{16}}{\frac{2}{2}+\frac{1}{2}}$$

Since \frac{2}{2} and \frac{1}{2} have the same denominator, add them by adding their numerators.

$$\frac{\frac{15}{16}}{\frac{2+1}{2}}$$

Add 2 and 1 to get 3.

$$\frac{\frac{15}{16}}{\frac{3}{2}}$$

Divide \frac{15}{16} by \frac{3}{2} by multiplying \frac{15}{16} by the reciprocal of \frac{3}{2}.

$$\frac{15}{16}\times \frac{2}{3}$$

Multiply \frac{15}{16} times \frac{2}{3} by multiplying numerator times numerator and denominator times denominator.

$$\frac{15\times 2}{16\times 3}$$

Do the multiplications in the fraction \frac{15\times 2}{16\times 3}.

$$\frac{30}{48}$$

Reduce the fraction \frac{30}{48} to lowest terms by extracting and canceling out 6.

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

Factor

$$\frac{5}{2 ^ {3}} = 0.625$$