Solve (174-2^{4}*7)^{2}:31-[5+3*4+(11+4^2*4^0)]-[14-(3^2+2)]^2

$$( 174 - 2 ^ { 4 } \times 7 ) ^ { 2 } : 31 - [ 5 + 3 \times 4 + ( 11 + 4 ^ { 2 } \times 4 ^ { 0 } ) ] - [ 14 - ( 3 ^ { 2 } + 2 ) ] ^ { 2 }$$

Evaluate

$$71$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 2 and 0 to get 2.

$$\frac{\left(174-2^{4}\times 7\right)^{2}}{31}-\left(5+3\times 4+11+4^{2}\right)-\left(14-\left(3^{2}+2\right)\right)^{2}$$

Calculate 2 to the power of 4 and get 16.

$$\frac{\left(174-16\times 7\right)^{2}}{31}-\left(5+3\times 4+11+4^{2}\right)-\left(14-\left(3^{2}+2\right)\right)^{2}$$

Multiply 16 and 7 to get 112.

$$\frac{\left(174-112\right)^{2}}{31}-\left(5+3\times 4+11+4^{2}\right)-\left(14-\left(3^{2}+2\right)\right)^{2}$$

Subtract 112 from 174 to get 62.

$$\frac{62^{2}}{31}-\left(5+3\times 4+11+4^{2}\right)-\left(14-\left(3^{2}+2\right)\right)^{2}$$

Calculate 62 to the power of 2 and get 3844.

$$\frac{3844}{31}-\left(5+3\times 4+11+4^{2}\right)-\left(14-\left(3^{2}+2\right)\right)^{2}$$

Divide 3844 by 31 to get 124.

$$124-\left(5+3\times 4+11+4^{2}\right)-\left(14-\left(3^{2}+2\right)\right)^{2}$$

Multiply 3 and 4 to get 12.

$$124-\left(5+12+11+4^{2}\right)-\left(14-\left(3^{2}+2\right)\right)^{2}$$

Add 5 and 12 to get 17.

$$124-\left(17+11+4^{2}\right)-\left(14-\left(3^{2}+2\right)\right)^{2}$$

Add 17 and 11 to get 28.

$$124-\left(28+4^{2}\right)-\left(14-\left(3^{2}+2\right)\right)^{2}$$

Calculate 4 to the power of 2 and get 16.

$$124-\left(28+16\right)-\left(14-\left(3^{2}+2\right)\right)^{2}$$

Add 28 and 16 to get 44.

$$124-44-\left(14-\left(3^{2}+2\right)\right)^{2}$$

Subtract 44 from 124 to get 80.

$$80-\left(14-\left(3^{2}+2\right)\right)^{2}$$

Calculate 3 to the power of 2 and get 9.

$$80-\left(14-\left(9+2\right)\right)^{2}$$

Add 9 and 2 to get 11.

$$80-\left(14-11\right)^{2}$$

Subtract 11 from 14 to get 3.

$$80-3^{2}$$

Calculate 3 to the power of 2 and get 9.

$$80-9$$

Subtract 9 from 80 to get 71.

$$71$$

Factor

$$71$$