Solve 2401(1-(-1/7)^5)/1+frac{1{7}}

$$\frac { 2401 ( 1 - ( - \frac { 1 } { 7 } ) ^ { 5 } ) } { 1 + \frac { 1 } { 7 } }$$

Evaluate

$$2101$$

Solution Steps

Calculate -\frac{1}{7} to the power of 5 and get -\frac{1}{16807}.

$$\frac{2401\left(1-\left(-\frac{1}{16807}\right)\right)}{1+\frac{1}{7}}$$

The opposite of -\frac{1}{16807} is \frac{1}{16807}.

$$\frac{2401\left(1+\frac{1}{16807}\right)}{1+\frac{1}{7}}$$

Convert 1 to fraction \frac{16807}{16807}.

$$\frac{2401\left(\frac{16807}{16807}+\frac{1}{16807}\right)}{1+\frac{1}{7}}$$

Since \frac{16807}{16807} and \frac{1}{16807} have the same denominator, add them by adding their numerators.

$$\frac{2401\times \frac{16807+1}{16807}}{1+\frac{1}{7}}$$

Add 16807 and 1 to get 16808.

$$\frac{2401\times \frac{16808}{16807}}{1+\frac{1}{7}}$$

Express 2401\times \frac{16808}{16807} as a single fraction.

$$\frac{\frac{2401\times 16808}{16807}}{1+\frac{1}{7}}$$

Multiply 2401 and 16808 to get 40356008.

$$\frac{\frac{40356008}{16807}}{1+\frac{1}{7}}$$

Reduce the fraction \frac{40356008}{16807} to lowest terms by extracting and canceling out 2401.

$$\frac{\frac{16808}{7}}{1+\frac{1}{7}}$$

Convert 1 to fraction \frac{7}{7}.

$$\frac{\frac{16808}{7}}{\frac{7}{7}+\frac{1}{7}}$$

Since \frac{7}{7} and \frac{1}{7} have the same denominator, add them by adding their numerators.

$$\frac{\frac{16808}{7}}{\frac{7+1}{7}}$$

Add 7 and 1 to get 8.

$$\frac{\frac{16808}{7}}{\frac{8}{7}}$$

Divide \frac{16808}{7} by \frac{8}{7} by multiplying \frac{16808}{7} by the reciprocal of \frac{8}{7}.

$$\frac{16808}{7}\times \frac{7}{8}$$

Multiply \frac{16808}{7} times \frac{7}{8} by multiplying numerator times numerator and denominator times denominator.

$$\frac{16808\times 7}{7\times 8}$$

Cancel out 7 in both numerator and denominator.

$$\frac{16808}{8}$$

Divide 16808 by 8 to get 2101.

$$2101$$

Factor

$$11\times 191$$