Solve 18!/4!0.1^40.9^14

$$\frac{ 18 ! }{ 4 ! } { 0.1 }^{ 4 } { 0.9 }^{ 14 }$$

Evaluate

$$6102740603.543292004488192$$

Solution Steps

The factorial of 18 is 6402373705728000.

$$\frac{6402373705728000}{4!}\times 0.1^{4}\times 0.9^{14}$$

The factorial of 4 is 24.

$$\frac{6402373705728000}{24}\times 0.1^{4}\times 0.9^{14}$$

Divide 6402373705728000 by 24 to get 266765571072000.

$$266765571072000\times 0.1^{4}\times 0.9^{14}$$

Calculate 0.1 to the power of 4 and get 0.0001.

$$266765571072000\times 0.0001\times 0.9^{14}$$

Multiply 266765571072000 and 0.0001 to get 26676557107.2.

$$26676557107.2\times 0.9^{14}$$

Calculate 0.9 to the power of 14 and get 0.22876792454961.

$$26676557107.2\times 0.22876792454961$$

Multiply 26676557107.2 and 0.22876792454961 to get 6102740603.543292004488192.

$$6102740603.543292004488192$$

Factor

$$\frac{11 \cdot 13 \cdot 17 \cdot 3 ^ {35} \cdot 7 ^ {2}}{2 ^ {5} \cdot 5 ^ {15}} = 6102740603\frac{530557593632}{976562500000} = 6102740603.543291$$