Solve 15!/1!14!0.7^10.3^14

$$\frac{ 15 ! }{ 1 ! 14 ! } { 0.7 }^{ 1 } { 0.3 }^{ 14 }$$

Evaluate

$$0.000000502211745$$

Solution Steps

The factorial of 15 is 1307674368000.

$$\frac{1307674368000}{1!\times 14!}\times 0.7^{1}\times 0.3^{14}$$

The factorial of 1 is 1.

$$\frac{1307674368000}{1\times 14!}\times 0.7^{1}\times 0.3^{14}$$

The factorial of 14 is 87178291200.

$$\frac{1307674368000}{1\times 87178291200}\times 0.7^{1}\times 0.3^{14}$$

Multiply 1 and 87178291200 to get 87178291200.

$$\frac{1307674368000}{87178291200}\times 0.7^{1}\times 0.3^{14}$$

Divide 1307674368000 by 87178291200 to get 15.

$$15\times 0.7^{1}\times 0.3^{14}$$

Calculate 0.7 to the power of 1 and get 0.7.

$$15\times 0.7\times 0.3^{14}$$

Multiply 15 and 0.7 to get 10.5.

$$10.5\times 0.3^{14}$$

Calculate 0.3 to the power of 14 and get 0.00000004782969.

$$10.5\times 0.00000004782969$$

Multiply 10.5 and 0.00000004782969 to get 0.000000502211745.

$$0.000000502211745$$

Factor

$$\frac{7 \cdot 3 ^ {15}}{2 ^ {15} \cdot 5 ^ {14}} = 5.02211745 \times 10^{-7}$$