Solve 6^{2}div11^4*12^3*7^8div180^2=

$$6 ^ { 2 } \div 11 ^ { 4 } \times 12 ^ { 3 } \times 7 ^ { 8 } \div 180 ^ { 2 } =$$

Evaluate

$$\frac{276710448}{366025}\approx 755.987836896$$

Solution Steps

Calculate 6 to the power of 2 and get 36.

$$\frac{\frac{36}{11^{4}}\times 12^{3}\times 7^{8}}{180^{2}}$$

Calculate 11 to the power of 4 and get 14641.

$$\frac{\frac{36}{14641}\times 12^{3}\times 7^{8}}{180^{2}}$$

Calculate 12 to the power of 3 and get 1728.

$$\frac{\frac{36}{14641}\times 1728\times 7^{8}}{180^{2}}$$

Express \frac{36}{14641}\times 1728 as a single fraction.

$$\frac{\frac{36\times 1728}{14641}\times 7^{8}}{180^{2}}$$

Multiply 36 and 1728 to get 62208.

$$\frac{\frac{62208}{14641}\times 7^{8}}{180^{2}}$$

Calculate 7 to the power of 8 and get 5764801.

$$\frac{\frac{62208}{14641}\times 5764801}{180^{2}}$$

Express \frac{62208}{14641}\times 5764801 as a single fraction.

$$\frac{\frac{62208\times 5764801}{14641}}{180^{2}}$$

Multiply 62208 and 5764801 to get 358616740608.

$$\frac{\frac{358616740608}{14641}}{180^{2}}$$

Calculate 180 to the power of 2 and get 32400.

$$\frac{\frac{358616740608}{14641}}{32400}$$

Express \frac{\frac{358616740608}{14641}}{32400} as a single fraction.

$$\frac{358616740608}{14641\times 32400}$$

Multiply 14641 and 32400 to get 474368400.

$$\frac{358616740608}{474368400}$$

Reduce the fraction \frac{358616740608}{474368400} to lowest terms by extracting and canceling out 1296.

$$\frac{276710448}{366025}$$

Factor

$$\frac{2 ^ {4} \cdot 3 \cdot 7 ^ {8}}{5 ^ {2} \cdot 11 ^ {4}} = 755\frac{361573}{366025} = 755.9878368963869$$