Solve [(2^{5}-2^{3}*3)^2-(10+4^2+3^3)+5^2]:12

$$[ ( 2 ^ { 5 } - 2 ^ { 3 } \times 3 ) ^ { 2 } - ( 10 + 4 ^ { 2 } + 3 ^ { 3 } ) + 5 ^ { 2 } ] : 12$$

Evaluate

$$3$$

Solution Steps

Calculate 2 to the power of 5 and get 32.

$$\frac{\left(32-2^{3}\times 3\right)^{2}-\left(10+4^{2}+3^{3}\right)+5^{2}}{12}$$

Calculate 2 to the power of 3 and get 8.

$$\frac{\left(32-8\times 3\right)^{2}-\left(10+4^{2}+3^{3}\right)+5^{2}}{12}$$

Multiply 8 and 3 to get 24.

$$\frac{\left(32-24\right)^{2}-\left(10+4^{2}+3^{3}\right)+5^{2}}{12}$$

Subtract 24 from 32 to get 8.

$$\frac{8^{2}-\left(10+4^{2}+3^{3}\right)+5^{2}}{12}$$

Calculate 8 to the power of 2 and get 64.

$$\frac{64-\left(10+4^{2}+3^{3}\right)+5^{2}}{12}$$

Calculate 4 to the power of 2 and get 16.

$$\frac{64-\left(10+16+3^{3}\right)+5^{2}}{12}$$

Add 10 and 16 to get 26.

$$\frac{64-\left(26+3^{3}\right)+5^{2}}{12}$$

Calculate 3 to the power of 3 and get 27.

$$\frac{64-\left(26+27\right)+5^{2}}{12}$$

Add 26 and 27 to get 53.

$$\frac{64-53+5^{2}}{12}$$

Subtract 53 from 64 to get 11.

$$\frac{11+5^{2}}{12}$$

Calculate 5 to the power of 2 and get 25.

$$\frac{11+25}{12}$$

Add 11 and 25 to get 36.

$$\frac{36}{12}$$

Divide 36 by 12 to get 3.

$$3$$

Factor

$$3$$