Solve (20*19)^5/100*99*98*97*96*95*94*93*92*91

$$\frac { ( 20 \times 19 ) ^ { 5 } } { 100 \times 99 \times 98 \times 97 \times 96 \times 95 \times 94 \times 93 \times 92 \times 91 }$$

Evaluate

$$\frac{3258025}{25828803846846}\approx 0.000000126$$

Solution Steps

Multiply 20 and 19 to get 380.

$$\frac{380^{5}}{100\times 99\times 98\times 97\times 96\times 95\times 94\times 93\times 92\times 91}$$

Calculate 380 to the power of 5 and get 7923516800000.

$$\frac{7923516800000}{100\times 99\times 98\times 97\times 96\times 95\times 94\times 93\times 92\times 91}$$

Multiply 100 and 99 to get 9900.

$$\frac{7923516800000}{9900\times 98\times 97\times 96\times 95\times 94\times 93\times 92\times 91}$$

Multiply 9900 and 98 to get 970200.

$$\frac{7923516800000}{970200\times 97\times 96\times 95\times 94\times 93\times 92\times 91}$$

Multiply 970200 and 97 to get 94109400.

$$\frac{7923516800000}{94109400\times 96\times 95\times 94\times 93\times 92\times 91}$$

Multiply 94109400 and 96 to get 9034502400.

$$\frac{7923516800000}{9034502400\times 95\times 94\times 93\times 92\times 91}$$

Multiply 9034502400 and 95 to get 858277728000.

$$\frac{7923516800000}{858277728000\times 94\times 93\times 92\times 91}$$

Multiply 858277728000 and 94 to get 80678106432000.

$$\frac{7923516800000}{80678106432000\times 93\times 92\times 91}$$

Multiply 80678106432000 and 93 to get 7503063898176000.

$$\frac{7923516800000}{7503063898176000\times 92\times 91}$$

Multiply 7503063898176000 and 92 to get 690281878632192000.

$$\frac{7923516800000}{690281878632192000\times 91}$$

Multiply 690281878632192000 and 91 to get 62815650955529472000.

$$\frac{7923516800000}{62815650955529472000}$$

Reduce the fraction \frac{7923516800000}{62815650955529472000} to lowest terms by extracting and canceling out 2432000.

$$\frac{3258025}{25828803846846}$$

Factor

$$\frac{5 ^ {2} \cdot 19 ^ {4}}{2 \cdot 3 ^ {4} \cdot 7 ^ {3} \cdot 11 \cdot 13 \cdot 23 \cdot 31 \cdot 47 \cdot 97} = 1.261392133882283 \times 10^{-7}$$