Solve 31096/3109^5+710930/71095-610918/61095

$$\frac { 31096 } { 3109 ^ { 5 } } + \frac { 710930 } { 71095 } - \frac { 610918 } { 61095 }$$

Evaluate

$$\frac{61181442791202370443052}{252335488222350596374152945}\approx 0.000242461$$

Solution Steps

Calculate 3109 to the power of 5 and get 290471555368654549.

$$\frac{31096}{290471555368654549}+\frac{710930}{71095}-\frac{610918}{61095}$$

Reduce the fraction \frac{710930}{71095} to lowest terms by extracting and canceling out 5.

$$\frac{31096}{290471555368654549}+\frac{142186}{14219}-\frac{610918}{61095}$$

Least common multiple of 290471555368654549 and 14219 is 4130215045786899032231. Convert \frac{31096}{290471555368654549} and \frac{142186}{14219} to fractions with denominator 4130215045786899032231.

$$\frac{442154024}{4130215045786899032231}+\frac{41300988571647515704114}{4130215045786899032231}-\frac{610918}{61095}$$

Since \frac{442154024}{4130215045786899032231} and \frac{41300988571647515704114}{4130215045786899032231} have the same denominator, add them by adding their numerators.

$$\frac{442154024+41300988571647515704114}{4130215045786899032231}-\frac{610918}{61095}$$

Add 442154024 and 41300988571647515704114 to get 41300988571647957858138.

$$\frac{41300988571647957858138}{4130215045786899032231}-\frac{610918}{61095}$$

Least common multiple of 4130215045786899032231 and 61095 is 252335488222350596374152945. Convert \frac{41300988571647957858138}{4130215045786899032231} and \frac{610918}{61095} to fractions with denominator 252335488222350596374152945.

$$\frac{2523283896784831985342941110}{252335488222350596374152945}-\frac{2523222715342040782972498058}{252335488222350596374152945}$$

Since \frac{2523283896784831985342941110}{252335488222350596374152945} and \frac{2523222715342040782972498058}{252335488222350596374152945} have the same denominator, subtract them by subtracting their numerators.

$$\frac{2523283896784831985342941110-2523222715342040782972498058}{252335488222350596374152945}$$

Subtract 2523222715342040782972498058 from 2523283896784831985342941110 to get 61181442791202370443052.

$$\frac{61181442791202370443052}{252335488222350596374152945}$$

Factor

$$\frac{2 ^ {2} \cdot 15295360697800592610763}{3 \cdot 5 \cdot 59 \cdot 241 \cdot 3109 ^ {5} \cdot 4073} = 0.00024246071459156426$$