Solve 1/(1+2^32)+1/12^13

$$\frac { 1 } { ( 1 + 2 ^ { 32 } ) } + \frac { 1 } { 12 ^ { 13 } }$$

Evaluate

$$\frac{106997500346369}{459532318104318728208384}\approx 2.3283999 \cdot 10^{-10}$$

Solution Steps

Calculate 2 to the power of 32 and get 4294967296.

$$\frac{1}{1+4294967296}+\frac{1}{12^{13}}$$

Add 1 and 4294967296 to get 4294967297.

$$\frac{1}{4294967297}+\frac{1}{12^{13}}$$

Calculate 12 to the power of 13 and get 106993205379072.

$$\frac{1}{4294967297}+\frac{1}{106993205379072}$$

Least common multiple of 4294967297 and 106993205379072 is 459532318104318728208384. Convert \frac{1}{4294967297} and \frac{1}{106993205379072} to fractions with denominator 459532318104318728208384.

$$\frac{106993205379072}{459532318104318728208384}+\frac{4294967297}{459532318104318728208384}$$

Since \frac{106993205379072}{459532318104318728208384} and \frac{4294967297}{459532318104318728208384} have the same denominator, add them by adding their numerators.

$$\frac{106993205379072+4294967297}{459532318104318728208384}$$

Add 106993205379072 and 4294967297 to get 106997500346369.

$$\frac{106997500346369}{459532318104318728208384}$$

Factor

$$\frac{19 \cdot 29 \cdot 194187840919}{2 ^ {26} \cdot 3 ^ {13} \cdot 641 \cdot 6700417} = 2.328399899875582 \times 10^{-10}$$