Solve 8[(2^{5}-2^{3}*3)^2-(10+4^2+3^3)+5^2]12

$$8 [ ( 2 ^ { 5 } - 2 ^ { 3 } \cdot 3 ) ^ { 2 } - ( 10 + 4 ^ { 2 } + 3 ^ { 3 } ) + 5 ^ { 2 } ] 12$$

Evaluate

$$3456$$

Solution Steps

Calculate 2 to the power of 5 and get 32.

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

Calculate 2 to the power of 3 and get 8.

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

Multiply 8 and 3 to get 24.

$$8\left(\left(32-24\right)^{2}-\left(10+4^{2}+3^{3}\right)+5^{2}\right)\times 12$$

Subtract 24 from 32 to get 8.

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

Calculate 8 to the power of 2 and get 64.

$$8\left(64-\left(10+4^{2}+3^{3}\right)+5^{2}\right)\times 12$$

Calculate 4 to the power of 2 and get 16.

$$8\left(64-\left(10+16+3^{3}\right)+5^{2}\right)\times 12$$

Add 10 and 16 to get 26.

$$8\left(64-\left(26+3^{3}\right)+5^{2}\right)\times 12$$

Calculate 3 to the power of 3 and get 27.

$$8\left(64-\left(26+27\right)+5^{2}\right)\times 12$$

Add 26 and 27 to get 53.

$$8\left(64-53+5^{2}\right)\times 12$$

Subtract 53 from 64 to get 11.

$$8\left(11+5^{2}\right)\times 12$$

Calculate 5 to the power of 2 and get 25.

$$8\left(11+25\right)\times 12$$

Add 11 and 25 to get 36.

$$8\times 36\times 12$$

Multiply 8 and 36 to get 288.

$$288\times 12$$

Multiply 288 and 12 to get 3456.

$$3456$$

Factor

$$2^{7}\times 3^{3}$$