Solve (1-1/2)(1+1/2)(1+1/4)(1+1/16)

$$( 1 - \frac { 1 } { 2 } ) ( 1 + \frac { 1 } { 2 } ) ( 1 + \frac { 1 } { 4 } ) ( 1 + \frac { 1 } { 16 } )$$

Evaluate

$$\frac{255}{256}=0.99609375$$

Solution Steps

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

$$\left(\frac{2}{2}-\frac{1}{2}\right)\left(1+\frac{1}{2}\right)\left(1+\frac{1}{4}\right)\left(1+\frac{1}{16}\right)$$

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

$$\frac{2-1}{2}\left(1+\frac{1}{2}\right)\left(1+\frac{1}{4}\right)\left(1+\frac{1}{16}\right)$$

Subtract 1 from 2 to get 1.

$$\frac{1}{2}\left(1+\frac{1}{2}\right)\left(1+\frac{1}{4}\right)\left(1+\frac{1}{16}\right)$$

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

$$\frac{1}{2}\left(\frac{2}{2}+\frac{1}{2}\right)\left(1+\frac{1}{4}\right)\left(1+\frac{1}{16}\right)$$

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

$$\frac{1}{2}\times \frac{2+1}{2}\left(1+\frac{1}{4}\right)\left(1+\frac{1}{16}\right)$$

Add 2 and 1 to get 3.

$$\frac{1}{2}\times \frac{3}{2}\left(1+\frac{1}{4}\right)\left(1+\frac{1}{16}\right)$$

Multiply \frac{1}{2} times \frac{3}{2} by multiplying numerator times numerator and denominator times denominator.

$$\frac{1\times 3}{2\times 2}\left(1+\frac{1}{4}\right)\left(1+\frac{1}{16}\right)$$

Do the multiplications in the fraction \frac{1\times 3}{2\times 2}.

$$\frac{3}{4}\left(1+\frac{1}{4}\right)\left(1+\frac{1}{16}\right)$$

Convert 1 to fraction \frac{4}{4}.

$$\frac{3}{4}\left(\frac{4}{4}+\frac{1}{4}\right)\left(1+\frac{1}{16}\right)$$

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

$$\frac{3}{4}\times \frac{4+1}{4}\left(1+\frac{1}{16}\right)$$

Add 4 and 1 to get 5.

$$\frac{3}{4}\times \frac{5}{4}\left(1+\frac{1}{16}\right)$$

Multiply \frac{3}{4} times \frac{5}{4} by multiplying numerator times numerator and denominator times denominator.

$$\frac{3\times 5}{4\times 4}\left(1+\frac{1}{16}\right)$$

Do the multiplications in the fraction \frac{3\times 5}{4\times 4}.

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

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

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

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

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

Add 16 and 1 to get 17.

$$\frac{15}{16}\times \frac{17}{16}$$

Multiply \frac{15}{16} times \frac{17}{16} by multiplying numerator times numerator and denominator times denominator.

$$\frac{15\times 17}{16\times 16}$$

Do the multiplications in the fraction \frac{15\times 17}{16\times 16}.

$$\frac{255}{256}$$

Factor

$$\frac{3 \cdot 5 \cdot 17}{2 ^ {8}} = 0.99609375$$