Solve frac{2^{3}*3^{2}*4^{2}*5^{2}}{5^3*4^3*2^6*3^4}

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

Evaluate

$$\frac{1}{1440}\approx 0.000694444$$

Solution Steps

Cancel out 2^{3}\times 3^{2}\times 4^{2}\times 5^{2} in both numerator and denominator.

$$\frac{1}{4\times 5\times 2^{3}\times 3^{2}}$$

Multiply 4 and 5 to get 20.

$$\frac{1}{20\times 2^{3}\times 3^{2}}$$

Calculate 2 to the power of 3 and get 8.

$$\frac{1}{20\times 8\times 3^{2}}$$

Multiply 20 and 8 to get 160.

$$\frac{1}{160\times 3^{2}}$$

Calculate 3 to the power of 2 and get 9.

$$\frac{1}{160\times 9}$$

Multiply 160 and 9 to get 1440.

$$\frac{1}{1440}$$

Factor

$$\frac{1}{2 ^ {5} \cdot 3 ^ {2} \cdot 5} = 0.0006944444444444445$$