Solve frac{(3^{4}3^{4}5^{2})^6}{(5^23^2)^4}=

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

Evaluate

$$7598540911910580500625$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 4 and 4 to get 8.

$$\frac{\left(3^{8}\times 5^{2}\right)^{6}}{\left(5^{2}\times 3^{2}\right)^{4}}$$

Calculate 3 to the power of 8 and get 6561.

$$\frac{\left(6561\times 5^{2}\right)^{6}}{\left(5^{2}\times 3^{2}\right)^{4}}$$

Calculate 5 to the power of 2 and get 25.

$$\frac{\left(6561\times 25\right)^{6}}{\left(5^{2}\times 3^{2}\right)^{4}}$$

Multiply 6561 and 25 to get 164025.

$$\frac{164025^{6}}{\left(5^{2}\times 3^{2}\right)^{4}}$$

Calculate 164025 to the power of 6 and get 19474229266814577603359619140625.

$$\frac{19474229266814577603359619140625}{\left(5^{2}\times 3^{2}\right)^{4}}$$

Calculate 5 to the power of 2 and get 25.

$$\frac{19474229266814577603359619140625}{\left(25\times 3^{2}\right)^{4}}$$

Calculate 3 to the power of 2 and get 9.

$$\frac{19474229266814577603359619140625}{\left(25\times 9\right)^{4}}$$

Multiply 25 and 9 to get 225.

$$\frac{19474229266814577603359619140625}{225^{4}}$$

Calculate 225 to the power of 4 and get 2562890625.

$$\frac{19474229266814577603359619140625}{2562890625}$$

Divide 19474229266814577603359619140625 by 2562890625 to get 7598540911910580500625.

$$7598540911910580500625$$

Factor

$$3^{40}\times 5^{4}$$