Solve frac{25^{2}*2^{3}*6^2}{3^3*8^2*5^4}=

$$\frac { 25 ^ { 2 } \cdot 2 ^ { 3 } \cdot 6 ^ { 2 } } { 3 ^ { 3 } \cdot 8 ^ { 2 } \cdot 5 ^ { 4 } } =$$

Evaluate

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

Solution Steps

Calculate 25 to the power of 2 and get 625.

$$\frac{625\times 2^{3}\times 6^{2}}{3^{3}\times 8^{2}\times 5^{4}}$$

Calculate 2 to the power of 3 and get 8.

$$\frac{625\times 8\times 6^{2}}{3^{3}\times 8^{2}\times 5^{4}}$$

Multiply 625 and 8 to get 5000.

$$\frac{5000\times 6^{2}}{3^{3}\times 8^{2}\times 5^{4}}$$

Calculate 6 to the power of 2 and get 36.

$$\frac{5000\times 36}{3^{3}\times 8^{2}\times 5^{4}}$$

Multiply 5000 and 36 to get 180000.

$$\frac{180000}{3^{3}\times 8^{2}\times 5^{4}}$$

Calculate 3 to the power of 3 and get 27.

$$\frac{180000}{27\times 8^{2}\times 5^{4}}$$

Calculate 8 to the power of 2 and get 64.

$$\frac{180000}{27\times 64\times 5^{4}}$$

Multiply 27 and 64 to get 1728.

$$\frac{180000}{1728\times 5^{4}}$$

Calculate 5 to the power of 4 and get 625.

$$\frac{180000}{1728\times 625}$$

Multiply 1728 and 625 to get 1080000.

$$\frac{180000}{1080000}$$

Reduce the fraction \frac{180000}{1080000} to lowest terms by extracting and canceling out 180000.

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

Factor

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