Solve (2^2*3)*7^4*(2*3)^2/2*(7*3*2)^4

$$\frac { ( 2 ^ { 2 } \cdot 3 ) \cdot 7 ^ { 4 } \cdot ( 2 \cdot 3 ) ^ { 2 } } { 2 \cdot ( 7 \cdot 3 \cdot 2 ) ^ { 4 } }$$

Evaluate

$$\frac{1}{6}\approx 0.166666667$$

Solution Steps

Cancel out 2 in both numerator and denominator.

$$\frac{2\times 3\times 7^{4}\times \left(2\times 3\right)^{2}}{\left(2\times 3\times 7\right)^{4}}$$

Multiply 2 and 3 to get 6.

$$\frac{6\times 7^{4}\times \left(2\times 3\right)^{2}}{\left(2\times 3\times 7\right)^{4}}$$

Calculate 7 to the power of 4 and get 2401.

$$\frac{6\times 2401\times \left(2\times 3\right)^{2}}{\left(2\times 3\times 7\right)^{4}}$$

Multiply 6 and 2401 to get 14406.

$$\frac{14406\times \left(2\times 3\right)^{2}}{\left(2\times 3\times 7\right)^{4}}$$

Multiply 2 and 3 to get 6.

$$\frac{14406\times 6^{2}}{\left(2\times 3\times 7\right)^{4}}$$

Calculate 6 to the power of 2 and get 36.

$$\frac{14406\times 36}{\left(2\times 3\times 7\right)^{4}}$$

Multiply 14406 and 36 to get 518616.

$$\frac{518616}{\left(2\times 3\times 7\right)^{4}}$$

Multiply 2 and 3 to get 6.

$$\frac{518616}{\left(6\times 7\right)^{4}}$$

Multiply 6 and 7 to get 42.

$$\frac{518616}{42^{4}}$$

Calculate 42 to the power of 4 and get 3111696.

$$\frac{518616}{3111696}$$

Reduce the fraction \frac{518616}{3111696} to lowest terms by extracting and canceling out 518616.

$$\frac{1}{6}$$

Factor

$$\frac{1}{2 \cdot 3} = 0.16666666666666666$$