Solve 48(1-(-1/2)^8)/frac{3{2}}

$$\frac { 48 ( 1 - ( - \frac { 1 } { 2 } ) ^ { 8 } ) } { \frac { 3 } { 2 } }$$

Evaluate

$$\frac{255}{8}=31.875$$

Solution Steps

Calculate -\frac{1}{2} to the power of 8 and get \frac{1}{256}.

$$\frac{48\left(1-\frac{1}{256}\right)}{\frac{3}{2}}$$

Convert 1 to fraction \frac{256}{256}.

$$\frac{48\left(\frac{256}{256}-\frac{1}{256}\right)}{\frac{3}{2}}$$

Since \frac{256}{256} and \frac{1}{256} have the same denominator, subtract them by subtracting their numerators.

$$\frac{48\times \frac{256-1}{256}}{\frac{3}{2}}$$

Subtract 1 from 256 to get 255.

$$\frac{48\times \frac{255}{256}}{\frac{3}{2}}$$

Express 48\times \frac{255}{256} as a single fraction.

$$\frac{\frac{48\times 255}{256}}{\frac{3}{2}}$$

Multiply 48 and 255 to get 12240.

$$\frac{\frac{12240}{256}}{\frac{3}{2}}$$

Reduce the fraction \frac{12240}{256} to lowest terms by extracting and canceling out 16.

$$\frac{\frac{765}{16}}{\frac{3}{2}}$$

Divide \frac{765}{16} by \frac{3}{2} by multiplying \frac{765}{16} by the reciprocal of \frac{3}{2}.

$$\frac{765}{16}\times \frac{2}{3}$$

Multiply \frac{765}{16} times \frac{2}{3} by multiplying numerator times numerator and denominator times denominator.

$$\frac{765\times 2}{16\times 3}$$

Do the multiplications in the fraction \frac{765\times 2}{16\times 3}.

$$\frac{1530}{48}$$

Reduce the fraction \frac{1530}{48} to lowest terms by extracting and canceling out 6.

$$\frac{255}{8}$$

Factor

$$\frac{3 \cdot 5 \cdot 17}{2 ^ {3}} = 31\frac{7}{8} = 31.875$$