Solve 1/1*2/9r*[-1-(-frac{1{2})^9}]

$$\frac { \frac { 1 } { 1 \times 2 } } { 9 r \cdot [ - 1 - ( - \frac { 1 } { 2 } ) ^ { 9 } } ]$$

Evaluate

$$-\frac{256}{4599r}$$

Solution Steps

Multiply 1 and 2 to get 2.

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

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

$$\frac{\frac{1}{2}}{9r\left(-1-\left(-\frac{1}{512}\right)\right)}$$

The opposite of -\frac{1}{512} is \frac{1}{512}.

$$\frac{\frac{1}{2}}{9r\left(-1+\frac{1}{512}\right)}$$

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

$$\frac{\frac{1}{2}}{9r\left(-\frac{512}{512}+\frac{1}{512}\right)}$$

Since -\frac{512}{512} and \frac{1}{512} have the same denominator, add them by adding their numerators.

$$\frac{\frac{1}{2}}{9r\times \frac{-512+1}{512}}$$

Add -512 and 1 to get -511.

$$\frac{\frac{1}{2}}{9r\left(-\frac{511}{512}\right)}$$

Express 9\left(-\frac{511}{512}\right) as a single fraction.

$$\frac{\frac{1}{2}}{\frac{9\left(-511\right)}{512}r}$$

Multiply 9 and -511 to get -4599.

$$\frac{\frac{1}{2}}{\frac{-4599}{512}r}$$

Fraction \frac{-4599}{512} can be rewritten as -\frac{4599}{512} by extracting the negative sign.

$$\frac{\frac{1}{2}}{-\frac{4599}{512}r}$$

Express \frac{\frac{1}{2}}{-\frac{4599}{512}r} as a single fraction.

$$\frac{1}{2\left(-\frac{4599}{512}\right)r}$$

Express 2\left(-\frac{4599}{512}\right) as a single fraction.

$$\frac{1}{\frac{2\left(-4599\right)}{512}r}$$

Multiply 2 and -4599 to get -9198.

$$\frac{1}{\frac{-9198}{512}r}$$

Reduce the fraction \frac{-9198}{512} to lowest terms by extracting and canceling out 2.

$$\frac{1}{-\frac{4599}{256}r}$$

Expand

$$-\frac{256}{4599r}$$

Solution Steps

Multiply 1 and 2 to get 2.

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

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

$$\frac{\frac{1}{2}}{9r\left(-1-\left(-\frac{1}{512}\right)\right)}$$

The opposite of -\frac{1}{512} is \frac{1}{512}.

$$\frac{\frac{1}{2}}{9r\left(-1+\frac{1}{512}\right)}$$

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

$$\frac{\frac{1}{2}}{9r\left(-\frac{512}{512}+\frac{1}{512}\right)}$$

Since -\frac{512}{512} and \frac{1}{512} have the same denominator, add them by adding their numerators.

$$\frac{\frac{1}{2}}{9r\times \frac{-512+1}{512}}$$

Add -512 and 1 to get -511.

$$\frac{\frac{1}{2}}{9r\left(-\frac{511}{512}\right)}$$

Express 9\left(-\frac{511}{512}\right) as a single fraction.

$$\frac{\frac{1}{2}}{\frac{9\left(-511\right)}{512}r}$$

Multiply 9 and -511 to get -4599.

$$\frac{\frac{1}{2}}{\frac{-4599}{512}r}$$

Fraction \frac{-4599}{512} can be rewritten as -\frac{4599}{512} by extracting the negative sign.

$$\frac{\frac{1}{2}}{-\frac{4599}{512}r}$$

Express \frac{\frac{1}{2}}{-\frac{4599}{512}r} as a single fraction.

$$\frac{1}{2\left(-\frac{4599}{512}\right)r}$$

Express 2\left(-\frac{4599}{512}\right) as a single fraction.

$$\frac{1}{\frac{2\left(-4599\right)}{512}r}$$

Multiply 2 and -4599 to get -9198.

$$\frac{1}{\frac{-9198}{512}r}$$

Reduce the fraction \frac{-9198}{512} to lowest terms by extracting and canceling out 2.

$$\frac{1}{-\frac{4599}{256}r}$$