Solve -32(({left(frac{1/2right)}^9-1)}{1/2-1}

$$\frac{ -32(( { \left( \frac{ 1 }{ 2 } \right) }^{ 9 } -1) }{ \frac{ 1 }{ 2 } -1 }$$

Evaluate

$$-\frac{511}{8}=-63.875$$

Solution Steps

Calculate \frac{1}{2} to the power of 9 and get \frac{1}{512}.

$$\frac{-32\left(\frac{1}{512}-1\right)}{\frac{1}{2}-1}$$

Convert 1 to fraction \frac{512}{512}.

$$\frac{-32\left(\frac{1}{512}-\frac{512}{512}\right)}{\frac{1}{2}-1}$$

Since \frac{1}{512} and \frac{512}{512} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-32\times \frac{1-512}{512}}{\frac{1}{2}-1}$$

Subtract 512 from 1 to get -511.

$$\frac{-32\left(-\frac{511}{512}\right)}{\frac{1}{2}-1}$$

Express -32\left(-\frac{511}{512}\right) as a single fraction.

$$\frac{\frac{-32\left(-511\right)}{512}}{\frac{1}{2}-1}$$

Multiply -32 and -511 to get 16352.

$$\frac{\frac{16352}{512}}{\frac{1}{2}-1}$$

Reduce the fraction \frac{16352}{512} to lowest terms by extracting and canceling out 32.

$$\frac{\frac{511}{16}}{\frac{1}{2}-1}$$

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

$$\frac{\frac{511}{16}}{\frac{1}{2}-\frac{2}{2}}$$

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

$$\frac{\frac{511}{16}}{\frac{1-2}{2}}$$

Subtract 2 from 1 to get -1.

$$\frac{\frac{511}{16}}{-\frac{1}{2}}$$

Divide \frac{511}{16} by -\frac{1}{2} by multiplying \frac{511}{16} by the reciprocal of -\frac{1}{2}.

$$\frac{511}{16}\left(-2\right)$$

Express \frac{511}{16}\left(-2\right) as a single fraction.

$$\frac{511\left(-2\right)}{16}$$

Multiply 511 and -2 to get -1022.

$$\frac{-1022}{16}$$

Reduce the fraction \frac{-1022}{16} to lowest terms by extracting and canceling out 2.

$$-\frac{511}{8}$$

Factor

$$-\frac{511}{8} = -63\frac{7}{8} = -63.875$$