Solve (5^{2}+2^{2})^{2}:29-(5^3*3^3)^2:15^5

$$( 5 ^ { 2 } + 2 ^ { 2 } ) ^ { 2 } : 29 - ( 5 ^ { 3 } \times 3 ^ { 3 } ) ^ { 2 } : 15 ^ { 5 }$$

Evaluate

$$14$$

Solution Steps

Calculate 5 to the power of 2 and get 25.

$$\frac{\left(25+2^{2}\right)^{2}}{29}-\frac{\left(5^{3}\times 3^{3}\right)^{2}}{15^{5}}$$

Calculate 2 to the power of 2 and get 4.

$$\frac{\left(25+4\right)^{2}}{29}-\frac{\left(5^{3}\times 3^{3}\right)^{2}}{15^{5}}$$

Add 25 and 4 to get 29.

$$\frac{29^{2}}{29}-\frac{\left(5^{3}\times 3^{3}\right)^{2}}{15^{5}}$$

Calculate 29 to the power of 2 and get 841.

$$\frac{841}{29}-\frac{\left(5^{3}\times 3^{3}\right)^{2}}{15^{5}}$$

Divide 841 by 29 to get 29.

$$29-\frac{\left(5^{3}\times 3^{3}\right)^{2}}{15^{5}}$$

Calculate 5 to the power of 3 and get 125.

$$29-\frac{\left(125\times 3^{3}\right)^{2}}{15^{5}}$$

Calculate 3 to the power of 3 and get 27.

$$29-\frac{\left(125\times 27\right)^{2}}{15^{5}}$$

Multiply 125 and 27 to get 3375.

$$29-\frac{3375^{2}}{15^{5}}$$

Calculate 3375 to the power of 2 and get 11390625.

$$29-\frac{11390625}{15^{5}}$$

Calculate 15 to the power of 5 and get 759375.

$$29-\frac{11390625}{759375}$$

Divide 11390625 by 759375 to get 15.

$$29-15$$

Subtract 15 from 29 to get 14.

$$14$$

Factor

$$2\times 7$$