Solve (2*3)^3*(3*5)^4*(2*9)/(3*3)^2*(3*9)*(5*6)^2

$$\frac { ( 2 \times 3 ) ^ { 3 } \times ( 3 \times 5 ) ^ { 4 } \times ( 2 \times 9 ) } { ( 3 \times 3 ) ^ { 2 } \times ( 3 \times 9 ) \times ( 5 \times 6 ) ^ { 2 } }$$

Evaluate

$$100$$

Solution Steps

Cancel out 3\times 3 in both numerator and denominator.

$$\frac{2\times \left(2\times 3\right)^{3}\times \left(3\times 5\right)^{4}}{3\times \left(3\times 3\right)^{2}\times \left(5\times 6\right)^{2}}$$

Multiply 2 and 3 to get 6.

$$\frac{2\times 6^{3}\times \left(3\times 5\right)^{4}}{3\times \left(3\times 3\right)^{2}\times \left(5\times 6\right)^{2}}$$

Calculate 6 to the power of 3 and get 216.

$$\frac{2\times 216\times \left(3\times 5\right)^{4}}{3\times \left(3\times 3\right)^{2}\times \left(5\times 6\right)^{2}}$$

Multiply 2 and 216 to get 432.

$$\frac{432\times \left(3\times 5\right)^{4}}{3\times \left(3\times 3\right)^{2}\times \left(5\times 6\right)^{2}}$$

Multiply 3 and 5 to get 15.

$$\frac{432\times 15^{4}}{3\times \left(3\times 3\right)^{2}\times \left(5\times 6\right)^{2}}$$

Calculate 15 to the power of 4 and get 50625.

$$\frac{432\times 50625}{3\times \left(3\times 3\right)^{2}\times \left(5\times 6\right)^{2}}$$

Multiply 432 and 50625 to get 21870000.

$$\frac{21870000}{3\times \left(3\times 3\right)^{2}\times \left(5\times 6\right)^{2}}$$

Multiply 3 and 3 to get 9.

$$\frac{21870000}{3\times 9^{2}\times \left(5\times 6\right)^{2}}$$

Calculate 9 to the power of 2 and get 81.

$$\frac{21870000}{3\times 81\times \left(5\times 6\right)^{2}}$$

Multiply 3 and 81 to get 243.

$$\frac{21870000}{243\times \left(5\times 6\right)^{2}}$$

Multiply 5 and 6 to get 30.

$$\frac{21870000}{243\times 30^{2}}$$

Calculate 30 to the power of 2 and get 900.

$$\frac{21870000}{243\times 900}$$

Multiply 243 and 900 to get 218700.

$$\frac{21870000}{218700}$$

Divide 21870000 by 218700 to get 100.

$$100$$

Factor

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