Solve 8({left(frac{1/2right)}^5-1)}{1/2-1}=

$$\frac{ 8( { \left( \frac{ 1 }{ 2 } \right) }^{ 5 } -1) }{ \frac{ 1 }{ 2 } -1 } =$$

Evaluate

$$\frac{31}{2}=15.5$$

Solution Steps

Calculate \frac{1}{2} to the power of 5 and get \frac{1}{32}.

$$\frac{8\left(\frac{1}{32}-1\right)}{\frac{1}{2}-1}$$

Convert 1 to fraction \frac{32}{32}.

$$\frac{8\left(\frac{1}{32}-\frac{32}{32}\right)}{\frac{1}{2}-1}$$

Since \frac{1}{32} and \frac{32}{32} have the same denominator, subtract them by subtracting their numerators.

$$\frac{8\times \frac{1-32}{32}}{\frac{1}{2}-1}$$

Subtract 32 from 1 to get -31.

$$\frac{8\left(-\frac{31}{32}\right)}{\frac{1}{2}-1}$$

Express 8\left(-\frac{31}{32}\right) as a single fraction.

$$\frac{\frac{8\left(-31\right)}{32}}{\frac{1}{2}-1}$$

Multiply 8 and -31 to get -248.

$$\frac{\frac{-248}{32}}{\frac{1}{2}-1}$$

Reduce the fraction \frac{-248}{32} to lowest terms by extracting and canceling out 8.

$$\frac{-\frac{31}{4}}{\frac{1}{2}-1}$$

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

$$\frac{-\frac{31}{4}}{\frac{1}{2}-\frac{2}{2}}$$

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

$$\frac{-\frac{31}{4}}{\frac{1-2}{2}}$$

Subtract 2 from 1 to get -1.

$$\frac{-\frac{31}{4}}{-\frac{1}{2}}$$

Divide -\frac{31}{4} by -\frac{1}{2} by multiplying -\frac{31}{4} by the reciprocal of -\frac{1}{2}.

$$-\frac{31}{4}\left(-2\right)$$

Express -\frac{31}{4}\left(-2\right) as a single fraction.

$$\frac{-31\left(-2\right)}{4}$$

Multiply -31 and -2 to get 62.

$$\frac{62}{4}$$

Reduce the fraction \frac{62}{4} to lowest terms by extracting and canceling out 2.

$$\frac{31}{2}$$

Factor

$$\frac{31}{2} = 15\frac{1}{2} = 15.5$$