Solve 9!9!9!/18!5!4!

$$\frac { 9 ! 9 ! 9 ! } { 18 ! 5 ! 4 ! }$$

Evaluate

$$\frac{63}{24310}\approx 0.002591526$$

Solution Steps

Multiply 9! and 9! to get \left(9!\right)^{2}.

$$\frac{\left(9!\right)^{2}\times 9!}{18!\times 5!\times 4!}$$

To multiply powers of the same base, add their exponents. Add 2 and 1 to get 3.

$$\frac{\left(9!\right)^{3}}{18!\times 5!\times 4!}$$

The factorial of 9 is 362880.

$$\frac{362880^{3}}{18!\times 5!\times 4!}$$

Calculate 362880 to the power of 3 and get 47784725839872000.

$$\frac{47784725839872000}{18!\times 5!\times 4!}$$

The factorial of 18 is 6402373705728000.

$$\frac{47784725839872000}{6402373705728000\times 5!\times 4!}$$

The factorial of 5 is 120.

$$\frac{47784725839872000}{6402373705728000\times 120\times 4!}$$

Multiply 6402373705728000 and 120 to get 768284844687360000.

$$\frac{47784725839872000}{768284844687360000\times 4!}$$

The factorial of 4 is 24.

$$\frac{47784725839872000}{768284844687360000\times 24}$$

Multiply 768284844687360000 and 24 to get 18438836272496640000.

$$\frac{47784725839872000}{18438836272496640000}$$

Reduce the fraction \frac{47784725839872000}{18438836272496640000} to lowest terms by extracting and canceling out 758487711744000.

$$\frac{63}{24310}$$

Factor

$$\frac{3 ^ {2} \cdot 7}{2 \cdot 5 \cdot 11 \cdot 13 \cdot 17} = 0.002591526120937886$$