Solve {[5^{2}*2+7-(5*3^{2}+9)]^2+11^5:11^4}:2^2

$$\{ [ 5 ^ { 2 } \times 2 + 7 - ( 5 \times 3 ^ { 2 } + 9 ) ] ^ { 2 } + 11 ^ { 5 } : 11 ^ { 4 } \} : 2 ^ { 2 }$$

Evaluate

$$5$$

Solution Steps

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent. Subtract 4 from 5 to get 1.

$$\frac{\left(5^{2}\times 2+7-\left(5\times 3^{2}+9\right)\right)^{2}+11^{1}}{2^{2}}$$

Calculate 5 to the power of 2 and get 25.

$$\frac{\left(25\times 2+7-\left(5\times 3^{2}+9\right)\right)^{2}+11^{1}}{2^{2}}$$

Multiply 25 and 2 to get 50.

$$\frac{\left(50+7-\left(5\times 3^{2}+9\right)\right)^{2}+11^{1}}{2^{2}}$$

Add 50 and 7 to get 57.

$$\frac{\left(57-\left(5\times 3^{2}+9\right)\right)^{2}+11^{1}}{2^{2}}$$

Calculate 3 to the power of 2 and get 9.

$$\frac{\left(57-\left(5\times 9+9\right)\right)^{2}+11^{1}}{2^{2}}$$

Multiply 5 and 9 to get 45.

$$\frac{\left(57-\left(45+9\right)\right)^{2}+11^{1}}{2^{2}}$$

Add 45 and 9 to get 54.

$$\frac{\left(57-54\right)^{2}+11^{1}}{2^{2}}$$

Subtract 54 from 57 to get 3.

$$\frac{3^{2}+11^{1}}{2^{2}}$$

Calculate 3 to the power of 2 and get 9.

$$\frac{9+11^{1}}{2^{2}}$$

Calculate 11 to the power of 1 and get 11.

$$\frac{9+11}{2^{2}}$$

Add 9 and 11 to get 20.

$$\frac{20}{2^{2}}$$

Calculate 2 to the power of 2 and get 4.

$$\frac{20}{4}$$

Divide 20 by 4 to get 5.

$$5$$

Factor

$$5$$