Solve 201-{left(frac{4/5right)}^10}{1-4/5}

$$20 \frac{ 1- { \left( \frac{ 4 }{ 5 } \right) }^{ 10 } }{ 1- \frac{ 4 }{ 5 } }$$

Evaluate

$$\frac{34868196}{390625}=89.26258176$$

Solution Steps

Calculate \frac{4}{5} to the power of 10 and get \frac{1048576}{9765625}.

$$20\times \frac{1-\frac{1048576}{9765625}}{1-\frac{4}{5}}$$

Convert 1 to fraction \frac{9765625}{9765625}.

$$20\times \frac{\frac{9765625}{9765625}-\frac{1048576}{9765625}}{1-\frac{4}{5}}$$

Since \frac{9765625}{9765625} and \frac{1048576}{9765625} have the same denominator, subtract them by subtracting their numerators.

$$20\times \frac{\frac{9765625-1048576}{9765625}}{1-\frac{4}{5}}$$

Subtract 1048576 from 9765625 to get 8717049.

$$20\times \frac{\frac{8717049}{9765625}}{1-\frac{4}{5}}$$

Convert 1 to fraction \frac{5}{5}.

$$20\times \frac{\frac{8717049}{9765625}}{\frac{5}{5}-\frac{4}{5}}$$

Since \frac{5}{5} and \frac{4}{5} have the same denominator, subtract them by subtracting their numerators.

$$20\times \frac{\frac{8717049}{9765625}}{\frac{5-4}{5}}$$

Subtract 4 from 5 to get 1.

$$20\times \frac{\frac{8717049}{9765625}}{\frac{1}{5}}$$

Divide \frac{8717049}{9765625} by \frac{1}{5} by multiplying \frac{8717049}{9765625} by the reciprocal of \frac{1}{5}.

$$20\times \frac{8717049}{9765625}\times 5$$

Express \frac{8717049}{9765625}\times 5 as a single fraction.

$$20\times \frac{8717049\times 5}{9765625}$$

Multiply 8717049 and 5 to get 43585245.

$$20\times \frac{43585245}{9765625}$$

Reduce the fraction \frac{43585245}{9765625} to lowest terms by extracting and canceling out 5.

$$20\times \frac{8717049}{1953125}$$

Express 20\times \frac{8717049}{1953125} as a single fraction.

$$\frac{20\times 8717049}{1953125}$$

Multiply 20 and 8717049 to get 174340980.

$$\frac{174340980}{1953125}$$

Reduce the fraction \frac{174340980}{1953125} to lowest terms by extracting and canceling out 5.

$$\frac{34868196}{390625}$$

Factor

$$\frac{2 ^ {2} \cdot 3 ^ {2} \cdot 11 \cdot 191 \cdot 461}{5 ^ {8}} = 89\frac{102571}{390625} = 89.26258176$$