Solve 1296(1-(-1/6)^5)/1+frac{1{6}}

$$\frac { 1296 ( 1 - ( - \frac { 1 } { 6 } ) ^ { 5 } ) } { 1 + \frac { 1 } { 6 } }$$

Evaluate

$$1111$$

Solution Steps

Calculate -\frac{1}{6} to the power of 5 and get -\frac{1}{7776}.

$$\frac{1296\left(1-\left(-\frac{1}{7776}\right)\right)}{1+\frac{1}{6}}$$

The opposite of -\frac{1}{7776} is \frac{1}{7776}.

$$\frac{1296\left(1+\frac{1}{7776}\right)}{1+\frac{1}{6}}$$

Convert 1 to fraction \frac{7776}{7776}.

$$\frac{1296\left(\frac{7776}{7776}+\frac{1}{7776}\right)}{1+\frac{1}{6}}$$

Since \frac{7776}{7776} and \frac{1}{7776} have the same denominator, add them by adding their numerators.

$$\frac{1296\times \frac{7776+1}{7776}}{1+\frac{1}{6}}$$

Add 7776 and 1 to get 7777.

$$\frac{1296\times \frac{7777}{7776}}{1+\frac{1}{6}}$$

Express 1296\times \frac{7777}{7776} as a single fraction.

$$\frac{\frac{1296\times 7777}{7776}}{1+\frac{1}{6}}$$

Multiply 1296 and 7777 to get 10078992.

$$\frac{\frac{10078992}{7776}}{1+\frac{1}{6}}$$

Reduce the fraction \frac{10078992}{7776} to lowest terms by extracting and canceling out 1296.

$$\frac{\frac{7777}{6}}{1+\frac{1}{6}}$$

Convert 1 to fraction \frac{6}{6}.

$$\frac{\frac{7777}{6}}{\frac{6}{6}+\frac{1}{6}}$$

Since \frac{6}{6} and \frac{1}{6} have the same denominator, add them by adding their numerators.

$$\frac{\frac{7777}{6}}{\frac{6+1}{6}}$$

Add 6 and 1 to get 7.

$$\frac{\frac{7777}{6}}{\frac{7}{6}}$$

Divide \frac{7777}{6} by \frac{7}{6} by multiplying \frac{7777}{6} by the reciprocal of \frac{7}{6}.

$$\frac{7777}{6}\times \frac{6}{7}$$

Multiply \frac{7777}{6} times \frac{6}{7} by multiplying numerator times numerator and denominator times denominator.

$$\frac{7777\times 6}{6\times 7}$$

Cancel out 6 in both numerator and denominator.

$$\frac{7777}{7}$$

Divide 7777 by 7 to get 1111.

$$1111$$

Factor

$$11\times 101$$