Solve frac{100^{3}*21^{4}*27^2}{2*6^3*15^2*35^4}

$$\frac { 100 ^ { 3 } \cdot 21 ^ { 4 } \cdot 27 ^ { 2 } } { 2 \cdot 6 ^ { 3 } \cdot 15 ^ { 2 } \cdot 35 ^ { 4 } }$$

Evaluate

$$972$$

Solution Steps

Calculate 100 to the power of 3 and get 1000000.

$$\frac{1000000\times 21^{4}\times 27^{2}}{2\times 6^{3}\times 15^{2}\times 35^{4}}$$

Calculate 21 to the power of 4 and get 194481.

$$\frac{1000000\times 194481\times 27^{2}}{2\times 6^{3}\times 15^{2}\times 35^{4}}$$

Multiply 1000000 and 194481 to get 194481000000.

$$\frac{194481000000\times 27^{2}}{2\times 6^{3}\times 15^{2}\times 35^{4}}$$

Calculate 27 to the power of 2 and get 729.

$$\frac{194481000000\times 729}{2\times 6^{3}\times 15^{2}\times 35^{4}}$$

Multiply 194481000000 and 729 to get 141776649000000.

$$\frac{141776649000000}{2\times 6^{3}\times 15^{2}\times 35^{4}}$$

Calculate 6 to the power of 3 and get 216.

$$\frac{141776649000000}{2\times 216\times 15^{2}\times 35^{4}}$$

Multiply 2 and 216 to get 432.

$$\frac{141776649000000}{432\times 15^{2}\times 35^{4}}$$

Calculate 15 to the power of 2 and get 225.

$$\frac{141776649000000}{432\times 225\times 35^{4}}$$

Multiply 432 and 225 to get 97200.

$$\frac{141776649000000}{97200\times 35^{4}}$$

Calculate 35 to the power of 4 and get 1500625.

$$\frac{141776649000000}{97200\times 1500625}$$

Multiply 97200 and 1500625 to get 145860750000.

$$\frac{141776649000000}{145860750000}$$

Divide 141776649000000 by 145860750000 to get 972.

$$972$$

Factor

$$2^{2}\times 3^{5}$$