Solve 11!+10!/72!

$$\frac { 11 ! + 10 ! } { 72 ! }$$

Evaluate

$$\frac{1}{1406214597499772350398756025528978191614723227712956739230209595549915146127776153600000000000000}\approx 7.111290139 \cdot 10^{-97}$$

Solution Steps

The factorial of 11 is 39916800.

$$\frac{39916800+10!}{72!}$$

The factorial of 10 is 3628800.

$$\frac{39916800+3628800}{72!}$$

Add 39916800 and 3628800 to get 43545600.

$$\frac{43545600}{72!}$$

The factorial of 72 is 61234458376886086861524070385274672740778091784697328983823014963978384987221689274204160000000000000000.

$$\frac{43545600}{61234458376886086861524070385274672740778091784697328983823014963978384987221689274204160000000000000000}$$

Reduce the fraction \frac{43545600}{61234458376886086861524070385274672740778091784697328983823014963978384987221689274204160000000000000000} to lowest terms by extracting and canceling out 43545600.

$$\frac{1}{1406214597499772350398756025528978191614723227712956739230209595549915146127776153600000000000000}$$

Factor

$$\frac{1}{2 ^ {60} \cdot 3 ^ {29} \cdot 5 ^ {14} \cdot 7 ^ {10} \cdot 11 ^ {6} \cdot 13 ^ {5} \cdot 17 ^ {4} \cdot 19 ^ {3} \cdot 23 ^ {3} \cdot 29 ^ {2} \cdot 31 ^ {2} \cdot 37 \cdot 41 \cdot 43 \cdot 47 \cdot 53 \cdot 59 \cdot 61 \cdot 67 \cdot 71} = 7.1112901386316425 \times 10^{-97}$$