Solve 20!/5!15!0.25^50.75^15

$$\frac { 20 ! } { 5 ! 15 ! 0.25 ^ { 5 } 0.75 ^ { 15 } }$$

Evaluate

$$\frac{5682276092346368}{4782969}\approx 1188022772.53864033$$

Solution Steps

The factorial of 20 is 2432902008176640000.

$$\frac{2432902008176640000}{5!\times 15!\times 0.25^{5}\times 0.75^{15}}$$

The factorial of 5 is 120.

$$\frac{2432902008176640000}{120\times 15!\times 0.25^{5}\times 0.75^{15}}$$

The factorial of 15 is 1307674368000.

$$\frac{2432902008176640000}{120\times 1307674368000\times 0.25^{5}\times 0.75^{15}}$$

Multiply 120 and 1307674368000 to get 156920924160000.

$$\frac{2432902008176640000}{156920924160000\times 0.25^{5}\times 0.75^{15}}$$

Calculate 0.25 to the power of 5 and get 0.0009765625.

$$\frac{2432902008176640000}{156920924160000\times 0.0009765625\times 0.75^{15}}$$

Multiply 156920924160000 and 0.0009765625 to get 153243090000.

$$\frac{2432902008176640000}{153243090000\times 0.75^{15}}$$

Calculate 0.75 to the power of 15 and get 0.013363461010158061981201171875.

$$\frac{2432902008176640000}{153243090000\times 0.013363461010158061981201171875}$$

Multiply 153243090000 and 0.013363461010158061981201171875 to get 2047858058.29114280641078948974609375.

$$\frac{2432902008176640000}{2047858058.29114280641078948974609375}$$

Expand \frac{2432902008176640000}{2047858058.29114280641078948974609375} by multiplying both numerator and the denominator by 100000000000000000000000000.

$$\frac{243290200817664000000000000000000000000000000}{204785805829114280641078948974609375}$$

Reduce the fraction \frac{243290200817664000000000000000000000000000000}{204785805829114280641078948974609375} to lowest terms by extracting and canceling out 42815624736249446868896484375.

$$\frac{5682276092346368}{4782969}$$

Factor

$$\frac{17 \cdot 19 \cdot 2 ^ {44}}{3 ^ {14}} = 1188022772\frac{2576300}{4782969} = 1188022772.5386403$$