Solve -(256)32^{2}:8^{4}-[73-2*(3*3^4-3*2^3*10)-60]^2-(2*10^2+1)+2

$$- ( 256 ) 32 ^ { 2 } : 8 ^ { 4 } - [ 73 - 2 \times ( 3 \times 3 ^ { 4 } - 3 \times 2 ^ { 3 } \times 10 ) - 60 ] ^ { 2 } - ( 2 \times 10 ^ { 2 } + 1 ) + 2$$

Evaluate

$$-312$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 1 and 4 to get 5.

$$\frac{-256\times 32^{2}}{8^{4}}-\left(73-2\left(3^{5}-3\times 2^{3}\times 10\right)-60\right)^{2}-\left(2\times 10^{2}+1\right)+2$$

Calculate 32 to the power of 2 and get 1024.

$$\frac{-256\times 1024}{8^{4}}-\left(73-2\left(3^{5}-3\times 2^{3}\times 10\right)-60\right)^{2}-\left(2\times 10^{2}+1\right)+2$$

Multiply -256 and 1024 to get -262144.

$$\frac{-262144}{8^{4}}-\left(73-2\left(3^{5}-3\times 2^{3}\times 10\right)-60\right)^{2}-\left(2\times 10^{2}+1\right)+2$$

Calculate 8 to the power of 4 and get 4096.

$$\frac{-262144}{4096}-\left(73-2\left(3^{5}-3\times 2^{3}\times 10\right)-60\right)^{2}-\left(2\times 10^{2}+1\right)+2$$

Divide -262144 by 4096 to get -64.

$$-64-\left(73-2\left(3^{5}-3\times 2^{3}\times 10\right)-60\right)^{2}-\left(2\times 10^{2}+1\right)+2$$

Calculate 3 to the power of 5 and get 243.

$$-64-\left(73-2\left(243-3\times 2^{3}\times 10\right)-60\right)^{2}-\left(2\times 10^{2}+1\right)+2$$

Calculate 2 to the power of 3 and get 8.

$$-64-\left(73-2\left(243-3\times 8\times 10\right)-60\right)^{2}-\left(2\times 10^{2}+1\right)+2$$

Multiply 3 and 8 to get 24.

$$-64-\left(73-2\left(243-24\times 10\right)-60\right)^{2}-\left(2\times 10^{2}+1\right)+2$$

Multiply 24 and 10 to get 240.

$$-64-\left(73-2\left(243-240\right)-60\right)^{2}-\left(2\times 10^{2}+1\right)+2$$

Subtract 240 from 243 to get 3.

$$-64-\left(73-2\times 3-60\right)^{2}-\left(2\times 10^{2}+1\right)+2$$

Multiply 2 and 3 to get 6.

$$-64-\left(73-6-60\right)^{2}-\left(2\times 10^{2}+1\right)+2$$

Subtract 6 from 73 to get 67.

$$-64-\left(67-60\right)^{2}-\left(2\times 10^{2}+1\right)+2$$

Subtract 60 from 67 to get 7.

$$-64-7^{2}-\left(2\times 10^{2}+1\right)+2$$

Calculate 7 to the power of 2 and get 49.

$$-64-49-\left(2\times 10^{2}+1\right)+2$$

Subtract 49 from -64 to get -113.

$$-113-\left(2\times 10^{2}+1\right)+2$$

Calculate 10 to the power of 2 and get 100.

$$-113-\left(2\times 100+1\right)+2$$

Multiply 2 and 100 to get 200.

$$-113-\left(200+1\right)+2$$

Add 200 and 1 to get 201.

$$-113-201+2$$

Subtract 201 from -113 to get -314.

$$-314+2$$

Add -314 and 2 to get -312.

$$-312$$

Factor

$$-312$$