Solve 1000(1/2^9-1)/-0.5

$$\frac { 1000 ( \frac { 1 } { 2 ^ { 9 } } - 1 ) } { - 0.5 }$$

Evaluate

$$1996.09375$$

Solution Steps

Calculate 2 to the power of 9 and get 512.

$$\frac{1000\left(\frac{1}{512}-1\right)}{-0.5}$$

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

$$\frac{1000\left(\frac{1}{512}-\frac{512}{512}\right)}{-0.5}$$

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

$$\frac{1000\times \frac{1-512}{512}}{-0.5}$$

Subtract 512 from 1 to get -511.

$$\frac{1000\left(-\frac{511}{512}\right)}{-0.5}$$

Express 1000\left(-\frac{511}{512}\right) as a single fraction.

$$\frac{\frac{1000\left(-511\right)}{512}}{-0.5}$$

Multiply 1000 and -511 to get -511000.

$$\frac{\frac{-511000}{512}}{-0.5}$$

Reduce the fraction \frac{-511000}{512} to lowest terms by extracting and canceling out 8.

$$\frac{-\frac{63875}{64}}{-0.5}$$

Express \frac{-\frac{63875}{64}}{-0.5} as a single fraction.

$$\frac{-63875}{64\left(-0.5\right)}$$

Multiply 64 and -0.5 to get -32.

$$\frac{-63875}{-32}$$

Fraction \frac{-63875}{-32} can be simplified to \frac{63875}{32} by removing the negative sign from both the numerator and the denominator.

$$\frac{63875}{32}$$

Factor

$$\frac{7 \cdot 73 \cdot 5 ^ {3}}{2 ^ {5}} = 1996\frac{3}{32} = 1996.09375$$