Solve (-1/2)^6-1/-frac{1{3}-1}

$$\frac { ( - \frac { 1 } { 2 } ) ^ { 6 } - 1 } { - \frac { 1 } { 3 } - 1 }$$

Evaluate

$$\frac{189}{256}=0.73828125$$

Solution Steps

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

$$\frac{\frac{1}{64}-1}{-\frac{1}{3}-1}$$

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

$$\frac{\frac{1}{64}-\frac{64}{64}}{-\frac{1}{3}-1}$$

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

$$\frac{\frac{1-64}{64}}{-\frac{1}{3}-1}$$

Subtract 64 from 1 to get -63.

$$\frac{-\frac{63}{64}}{-\frac{1}{3}-1}$$

Convert 1 to fraction \frac{3}{3}.

$$\frac{-\frac{63}{64}}{-\frac{1}{3}-\frac{3}{3}}$$

Since -\frac{1}{3} and \frac{3}{3} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-\frac{63}{64}}{\frac{-1-3}{3}}$$

Subtract 3 from -1 to get -4.

$$\frac{-\frac{63}{64}}{-\frac{4}{3}}$$

Divide -\frac{63}{64} by -\frac{4}{3} by multiplying -\frac{63}{64} by the reciprocal of -\frac{4}{3}.

$$-\frac{63}{64}\left(-\frac{3}{4}\right)$$

Multiply -\frac{63}{64} times -\frac{3}{4} by multiplying numerator times numerator and denominator times denominator.

$$\frac{-63\left(-3\right)}{64\times 4}$$

Do the multiplications in the fraction \frac{-63\left(-3\right)}{64\times 4}.

$$\frac{189}{256}$$

Factor

$$\frac{3 ^ {3} \cdot 7}{2 ^ {8}} = 0.73828125$$