Solve (9^{3}*3^{2})^{2}:3^{10}]^{2}:[(3^{3}*3^{3})^{0}:(3^5)^5]-(5^3)^2

$$( 9 ^ { 3 } \times 3 ^ { 2 } ) ^ { 2 } : 3 ^ { 10 } ] ^ { 2 } : [ ( 3 ^ { 3 } \times 3 ^ { 3 } ) ^ { 0 } : ( 3 ^ { 5 } ) ^ { 5 } ] - ( 5 ^ { 3 } ) ^ { 2 }$$

Evaluate

$$729$$

Solution Steps

Calculate 9 to the power of 3 and get 729.

$$\frac{\left(729\times 3^{2}\right)^{2}}{3^{10}}$$

Calculate 3 to the power of 2 and get 9.

$$\frac{\left(729\times 9\right)^{2}}{3^{10}}$$

Multiply 729 and 9 to get 6561.

$$\frac{6561^{2}}{3^{10}}$$

Calculate 6561 to the power of 2 and get 43046721.

$$\frac{43046721}{3^{10}}$$

Calculate 3 to the power of 10 and get 59049.

$$\frac{43046721}{59049}$$

Divide 43046721 by 59049 to get 729.

$$729$$

Factor

$$3^{6}$$