Solve 1/frac{1{37}-1/52^66}=

$$\frac { 1 } { \frac { 1 } { 37 } - \frac { 1 } { 52 ^ { 6 } 6 } } =$$

Evaluate

$$\frac{4389075345408}{118623657947}\approx 37.000000012$$

Solution Steps

Calculate 52 to the power of 6 and get 19770609664.

$$\frac{1}{\frac{1}{37}-\frac{1}{19770609664\times 6}}$$

Multiply 19770609664 and 6 to get 118623657984.

$$\frac{1}{\frac{1}{37}-\frac{1}{118623657984}}$$

Least common multiple of 37 and 118623657984 is 4389075345408. Convert \frac{1}{37} and \frac{1}{118623657984} to fractions with denominator 4389075345408.

$$\frac{1}{\frac{118623657984}{4389075345408}-\frac{37}{4389075345408}}$$

Since \frac{118623657984}{4389075345408} and \frac{37}{4389075345408} have the same denominator, subtract them by subtracting their numerators.

$$\frac{1}{\frac{118623657984-37}{4389075345408}}$$

Subtract 37 from 118623657984 to get 118623657947.

$$\frac{1}{\frac{118623657947}{4389075345408}}$$

Divide 1 by \frac{118623657947}{4389075345408} by multiplying 1 by the reciprocal of \frac{118623657947}{4389075345408}.

$$1\times \frac{4389075345408}{118623657947}$$

Multiply 1 and \frac{4389075345408}{118623657947} to get \frac{4389075345408}{118623657947}.

$$\frac{4389075345408}{118623657947}$$

Factor

$$\frac{2 ^ {13} \cdot 3 \cdot 13 ^ {6} \cdot 37}{2803 \cdot 42320249} = 37\frac{1369}{118623657947} = 37.0000000115407$$