Solve 8!/4!4!2^8

$$\frac{ 8 ! }{ 4 ! 4 ! { 2 }^{ 8 } }$$

Evaluate

$$\frac{35}{128}=0.2734375$$

Solution Steps

Multiply 4! and 4! to get \left(4!\right)^{2}.

$$\frac{8!}{\left(4!\right)^{2}\times 2^{8}}$$

The factorial of 8 is 40320.

$$\frac{40320}{\left(4!\right)^{2}\times 2^{8}}$$

The factorial of 4 is 24.

$$\frac{40320}{24^{2}\times 2^{8}}$$

Calculate 24 to the power of 2 and get 576.

$$\frac{40320}{576\times 2^{8}}$$

Calculate 2 to the power of 8 and get 256.

$$\frac{40320}{576\times 256}$$

Multiply 576 and 256 to get 147456.

$$\frac{40320}{147456}$$

Reduce the fraction \frac{40320}{147456} to lowest terms by extracting and canceling out 1152.

$$\frac{35}{128}$$

Factor

$$\frac{5 \cdot 7}{2 ^ {7}} = 0.2734375$$