Solve 6(1-(1/2)^6)

$$6 ( 1 - ( \frac { 1 } { 2 } ) ^ { 6 } )$$

Evaluate

$$\frac{189}{32}=5.90625$$

Solution Steps

Calculate \frac{1}{2} to the power of 6 and get \frac{1}{64}.

$$6\left(1-\frac{1}{64}\right)$$

Convert 1 to fraction \frac{64}{64}.

$$6\left(\frac{64}{64}-\frac{1}{64}\right)$$

Since \frac{64}{64} and \frac{1}{64} have the same denominator, subtract them by subtracting their numerators.

$$6\times \frac{64-1}{64}$$

Subtract 1 from 64 to get 63.

$$6\times \frac{63}{64}$$

Express 6\times \frac{63}{64} as a single fraction.

$$\frac{6\times 63}{64}$$

Multiply 6 and 63 to get 378.

$$\frac{378}{64}$$

Reduce the fraction \frac{378}{64} to lowest terms by extracting and canceling out 2.

$$\frac{189}{32}$$

Factor

$$\frac{3 ^ {3} \cdot 7}{2 ^ {5}} = 5\frac{29}{32} = 5.90625$$