Solve 1200*1-(51/50)^12/1-(frac{51{50})}=

$$1200 \times \frac { 1 - ( \frac { 51 } { 50 } ) ^ { 12 } } { 1 - ( \frac { 51 } { 50 } ) } =$$

Evaluate

$$\frac{196466158126864246803}{12207031250000000}=16094.507673753$$

Solution Steps

Calculate \frac{51}{50} to the power of 12 and get \frac{309629344375621415601}{244140625000000000000}.

$$1200\times \frac{1-\frac{309629344375621415601}{244140625000000000000}}{1-\frac{51}{50}}$$

Convert 1 to fraction \frac{244140625000000000000}{244140625000000000000}.

$$1200\times \frac{\frac{244140625000000000000}{244140625000000000000}-\frac{309629344375621415601}{244140625000000000000}}{1-\frac{51}{50}}$$

Since \frac{244140625000000000000}{244140625000000000000} and \frac{309629344375621415601}{244140625000000000000} have the same denominator, subtract them by subtracting their numerators.

$$1200\times \frac{\frac{244140625000000000000-309629344375621415601}{244140625000000000000}}{1-\frac{51}{50}}$$

Subtract 309629344375621415601 from 244140625000000000000 to get -65488719375621415601.

$$1200\times \frac{-\frac{65488719375621415601}{244140625000000000000}}{1-\frac{51}{50}}$$

Convert 1 to fraction \frac{50}{50}.

$$1200\times \frac{-\frac{65488719375621415601}{244140625000000000000}}{\frac{50}{50}-\frac{51}{50}}$$

Since \frac{50}{50} and \frac{51}{50} have the same denominator, subtract them by subtracting their numerators.

$$1200\times \frac{-\frac{65488719375621415601}{244140625000000000000}}{\frac{50-51}{50}}$$

Subtract 51 from 50 to get -1.

$$1200\times \frac{-\frac{65488719375621415601}{244140625000000000000}}{-\frac{1}{50}}$$

Divide -\frac{65488719375621415601}{244140625000000000000} by -\frac{1}{50} by multiplying -\frac{65488719375621415601}{244140625000000000000} by the reciprocal of -\frac{1}{50}.

$$1200\left(-\frac{65488719375621415601}{244140625000000000000}\right)\left(-50\right)$$

Express -\frac{65488719375621415601}{244140625000000000000}\left(-50\right) as a single fraction.

$$1200\times \frac{-65488719375621415601\left(-50\right)}{244140625000000000000}$$

Multiply -65488719375621415601 and -50 to get 3274435968781070780050.

$$1200\times \frac{3274435968781070780050}{244140625000000000000}$$

Reduce the fraction \frac{3274435968781070780050}{244140625000000000000} to lowest terms by extracting and canceling out 50.

$$1200\times \frac{65488719375621415601}{4882812500000000000}$$

Express 1200\times \frac{65488719375621415601}{4882812500000000000} as a single fraction.

$$\frac{1200\times 65488719375621415601}{4882812500000000000}$$

Multiply 1200 and 65488719375621415601 to get 78586463250745698721200.

$$\frac{78586463250745698721200}{4882812500000000000}$$

Reduce the fraction \frac{78586463250745698721200}{4882812500000000000} to lowest terms by extracting and canceling out 400.

$$\frac{196466158126864246803}{12207031250000000}$$

Factor

$$\frac{3 \cdot 7 \cdot 13 \cdot 101 \cdot 1093 \cdot 2551 \cdot 5101 \cdot 500977}{2 ^ {7} \cdot 5 ^ {20}} = 16094\frac{6197189364236544}{12207031250000000} = 16094.507673752718$$