Solve 10^1/9!*6!/2!4!/10^6

$$\frac { \frac { 10 ^ { 1 } } { 9 ! } \times \frac { 6 ! } { 2 ! 4 ! } } { 10 ^ { 6 } }$$

Evaluate

$$\frac{1}{2419200000}\approx 4.133597884 \cdot 10^{-10}$$

Solution Steps

Calculate 10 to the power of 1 and get 10.

$$\frac{\frac{10}{9!}\times \frac{6!}{2!\times 4!}}{10^{6}}$$

The factorial of 9 is 362880.

$$\frac{\frac{10}{362880}\times \frac{6!}{2!\times 4!}}{10^{6}}$$

Reduce the fraction \frac{10}{362880} to lowest terms by extracting and canceling out 10.

$$\frac{\frac{1}{36288}\times \frac{6!}{2!\times 4!}}{10^{6}}$$

The factorial of 6 is 720.

$$\frac{\frac{1}{36288}\times \frac{720}{2!\times 4!}}{10^{6}}$$

The factorial of 2 is 2.

$$\frac{\frac{1}{36288}\times \frac{720}{2\times 4!}}{10^{6}}$$

The factorial of 4 is 24.

$$\frac{\frac{1}{36288}\times \frac{720}{2\times 24}}{10^{6}}$$

Multiply 2 and 24 to get 48.

$$\frac{\frac{1}{36288}\times \frac{720}{48}}{10^{6}}$$

Divide 720 by 48 to get 15.

$$\frac{\frac{1}{36288}\times 15}{10^{6}}$$

Multiply \frac{1}{36288} and 15 to get \frac{15}{36288}.

$$\frac{\frac{15}{36288}}{10^{6}}$$

Reduce the fraction \frac{15}{36288} to lowest terms by extracting and canceling out 3.

$$\frac{\frac{5}{12096}}{10^{6}}$$

Calculate 10 to the power of 6 and get 1000000.

$$\frac{\frac{5}{12096}}{1000000}$$

Express \frac{\frac{5}{12096}}{1000000} as a single fraction.

$$\frac{5}{12096\times 1000000}$$

Multiply 12096 and 1000000 to get 12096000000.

$$\frac{5}{12096000000}$$

Reduce the fraction \frac{5}{12096000000} to lowest terms by extracting and canceling out 5.

$$\frac{1}{2419200000}$$

Factor

$$\frac{1}{2 ^ {12} \cdot 3 ^ {3} \cdot 5 ^ {5} \cdot 7} = 4.133597883597884 \times 10^{-10}$$