Solve {l}{(10^{2}-8^{2}):2+6^{2}:2-4^{2}*2-3*2^{0}}{5-4*5^{2}-12^{2}:4-(11^{2}*2-3^3*2-22*3):2}{(4^2*5-8^2:4):2-(5^2*2+3*5-2):3}

$$\left. \begin{array} { l } { ( 10 ^ { 2 } - 8 ^ { 2 } ) : 2 + 6 ^ { 2 } : 2 - 4 ^ { 2 } \cdot 2 - 3 \cdot 2 ^ { 0 } } \\ { 5 - 4 \cdot 5 ^ { 2 } - 12 ^ { 2 } : 4 - ( 11 ^ { 2 } \cdot 2 - 3 ^ { 3 } \cdot 2 - 22 \cdot 3 ) : 2 } \\ { ( 4 ^ { 2 } \cdot 5 - 8 ^ { 2 } : 4 ) : 2 - ( 5 ^ { 2 } \cdot 2 + 3 \cdot 5 - 2 ) : 3 } \end{array} \right.$$

Sort

$$-192,1,11$$

Solution Steps

Calculate 10 to the power of 2 and get 100.

$$sort(\frac{100-8^{2}}{2}+\frac{6^{2}}{2}-4^{2}\times 2-3\times 2^{0},5-4\times 5^{2}-\frac{12^{2}}{4}-\frac{11^{2}\times 2-3^{3}\times 2-22\times 3}{2},\frac{4^{2}\times 5-\frac{8^{2}}{4}}{2}-\frac{5^{2}\times 2+3\times 5-2}{3})$$

Calculate 8 to the power of 2 and get 64.

$$sort(\frac{100-64}{2}+\frac{6^{2}}{2}-4^{2}\times 2-3\times 2^{0},5-4\times 5^{2}-\frac{12^{2}}{4}-\frac{11^{2}\times 2-3^{3}\times 2-22\times 3}{2},\frac{4^{2}\times 5-\frac{8^{2}}{4}}{2}-\frac{5^{2}\times 2+3\times 5-2}{3})$$

Subtract 64 from 100 to get 36.

$$sort(\frac{36}{2}+\frac{6^{2}}{2}-4^{2}\times 2-3\times 2^{0},5-4\times 5^{2}-\frac{12^{2}}{4}-\frac{11^{2}\times 2-3^{3}\times 2-22\times 3}{2},\frac{4^{2}\times 5-\frac{8^{2}}{4}}{2}-\frac{5^{2}\times 2+3\times 5-2}{3})$$

Divide 36 by 2 to get 18.

$$sort(18+\frac{6^{2}}{2}-4^{2}\times 2-3\times 2^{0},5-4\times 5^{2}-\frac{12^{2}}{4}-\frac{11^{2}\times 2-3^{3}\times 2-22\times 3}{2},\frac{4^{2}\times 5-\frac{8^{2}}{4}}{2}-\frac{5^{2}\times 2+3\times 5-2}{3})$$

Calculate 6 to the power of 2 and get 36.

$$sort(18+\frac{36}{2}-4^{2}\times 2-3\times 2^{0},5-4\times 5^{2}-\frac{12^{2}}{4}-\frac{11^{2}\times 2-3^{3}\times 2-22\times 3}{2},\frac{4^{2}\times 5-\frac{8^{2}}{4}}{2}-\frac{5^{2}\times 2+3\times 5-2}{3})$$

Divide 36 by 2 to get 18.

$$sort(18+18-4^{2}\times 2-3\times 2^{0},5-4\times 5^{2}-\frac{12^{2}}{4}-\frac{11^{2}\times 2-3^{3}\times 2-22\times 3}{2},\frac{4^{2}\times 5-\frac{8^{2}}{4}}{2}-\frac{5^{2}\times 2+3\times 5-2}{3})$$

Add 18 and 18 to get 36.

$$sort(36-4^{2}\times 2-3\times 2^{0},5-4\times 5^{2}-\frac{12^{2}}{4}-\frac{11^{2}\times 2-3^{3}\times 2-22\times 3}{2},\frac{4^{2}\times 5-\frac{8^{2}}{4}}{2}-\frac{5^{2}\times 2+3\times 5-2}{3})$$

Calculate 4 to the power of 2 and get 16.

$$sort(36-16\times 2-3\times 2^{0},5-4\times 5^{2}-\frac{12^{2}}{4}-\frac{11^{2}\times 2-3^{3}\times 2-22\times 3}{2},\frac{4^{2}\times 5-\frac{8^{2}}{4}}{2}-\frac{5^{2}\times 2+3\times 5-2}{3})$$

Multiply 16 and 2 to get 32.

$$sort(36-32-3\times 2^{0},5-4\times 5^{2}-\frac{12^{2}}{4}-\frac{11^{2}\times 2-3^{3}\times 2-22\times 3}{2},\frac{4^{2}\times 5-\frac{8^{2}}{4}}{2}-\frac{5^{2}\times 2+3\times 5-2}{3})$$

Subtract 32 from 36 to get 4.

$$sort(4-3\times 2^{0},5-4\times 5^{2}-\frac{12^{2}}{4}-\frac{11^{2}\times 2-3^{3}\times 2-22\times 3}{2},\frac{4^{2}\times 5-\frac{8^{2}}{4}}{2}-\frac{5^{2}\times 2+3\times 5-2}{3})$$

Calculate 2 to the power of 0 and get 1.

$$sort(4-3\times 1,5-4\times 5^{2}-\frac{12^{2}}{4}-\frac{11^{2}\times 2-3^{3}\times 2-22\times 3}{2},\frac{4^{2}\times 5-\frac{8^{2}}{4}}{2}-\frac{5^{2}\times 2+3\times 5-2}{3})$$

Multiply 3 and 1 to get 3.

$$sort(4-3,5-4\times 5^{2}-\frac{12^{2}}{4}-\frac{11^{2}\times 2-3^{3}\times 2-22\times 3}{2},\frac{4^{2}\times 5-\frac{8^{2}}{4}}{2}-\frac{5^{2}\times 2+3\times 5-2}{3})$$

Subtract 3 from 4 to get 1.

$$sort(1,5-4\times 5^{2}-\frac{12^{2}}{4}-\frac{11^{2}\times 2-3^{3}\times 2-22\times 3}{2},\frac{4^{2}\times 5-\frac{8^{2}}{4}}{2}-\frac{5^{2}\times 2+3\times 5-2}{3})$$

Calculate 5 to the power of 2 and get 25.

$$sort(1,5-4\times 25-\frac{12^{2}}{4}-\frac{11^{2}\times 2-3^{3}\times 2-22\times 3}{2},\frac{4^{2}\times 5-\frac{8^{2}}{4}}{2}-\frac{5^{2}\times 2+3\times 5-2}{3})$$

Multiply 4 and 25 to get 100.

$$sort(1,5-100-\frac{12^{2}}{4}-\frac{11^{2}\times 2-3^{3}\times 2-22\times 3}{2},\frac{4^{2}\times 5-\frac{8^{2}}{4}}{2}-\frac{5^{2}\times 2+3\times 5-2}{3})$$

Subtract 100 from 5 to get -95.

$$sort(1,-95-\frac{12^{2}}{4}-\frac{11^{2}\times 2-3^{3}\times 2-22\times 3}{2},\frac{4^{2}\times 5-\frac{8^{2}}{4}}{2}-\frac{5^{2}\times 2+3\times 5-2}{3})$$

Calculate 12 to the power of 2 and get 144.

$$sort(1,-95-\frac{144}{4}-\frac{11^{2}\times 2-3^{3}\times 2-22\times 3}{2},\frac{4^{2}\times 5-\frac{8^{2}}{4}}{2}-\frac{5^{2}\times 2+3\times 5-2}{3})$$

Divide 144 by 4 to get 36.

$$sort(1,-95-36-\frac{11^{2}\times 2-3^{3}\times 2-22\times 3}{2},\frac{4^{2}\times 5-\frac{8^{2}}{4}}{2}-\frac{5^{2}\times 2+3\times 5-2}{3})$$

Subtract 36 from -95 to get -131.

$$sort(1,-131-\frac{11^{2}\times 2-3^{3}\times 2-22\times 3}{2},\frac{4^{2}\times 5-\frac{8^{2}}{4}}{2}-\frac{5^{2}\times 2+3\times 5-2}{3})$$

Calculate 11 to the power of 2 and get 121.

$$sort(1,-131-\frac{121\times 2-3^{3}\times 2-22\times 3}{2},\frac{4^{2}\times 5-\frac{8^{2}}{4}}{2}-\frac{5^{2}\times 2+3\times 5-2}{3})$$

Multiply 121 and 2 to get 242.

$$sort(1,-131-\frac{242-3^{3}\times 2-22\times 3}{2},\frac{4^{2}\times 5-\frac{8^{2}}{4}}{2}-\frac{5^{2}\times 2+3\times 5-2}{3})$$

Calculate 3 to the power of 3 and get 27.

$$sort(1,-131-\frac{242-27\times 2-22\times 3}{2},\frac{4^{2}\times 5-\frac{8^{2}}{4}}{2}-\frac{5^{2}\times 2+3\times 5-2}{3})$$

Multiply 27 and 2 to get 54.

$$sort(1,-131-\frac{242-54-22\times 3}{2},\frac{4^{2}\times 5-\frac{8^{2}}{4}}{2}-\frac{5^{2}\times 2+3\times 5-2}{3})$$

Subtract 54 from 242 to get 188.

$$sort(1,-131-\frac{188-22\times 3}{2},\frac{4^{2}\times 5-\frac{8^{2}}{4}}{2}-\frac{5^{2}\times 2+3\times 5-2}{3})$$

Multiply 22 and 3 to get 66.

$$sort(1,-131-\frac{188-66}{2},\frac{4^{2}\times 5-\frac{8^{2}}{4}}{2}-\frac{5^{2}\times 2+3\times 5-2}{3})$$

Subtract 66 from 188 to get 122.

$$sort(1,-131-\frac{122}{2},\frac{4^{2}\times 5-\frac{8^{2}}{4}}{2}-\frac{5^{2}\times 2+3\times 5-2}{3})$$

Divide 122 by 2 to get 61.

$$sort(1,-131-61,\frac{4^{2}\times 5-\frac{8^{2}}{4}}{2}-\frac{5^{2}\times 2+3\times 5-2}{3})$$

Subtract 61 from -131 to get -192.

$$sort(1,-192,\frac{4^{2}\times 5-\frac{8^{2}}{4}}{2}-\frac{5^{2}\times 2+3\times 5-2}{3})$$

Calculate 4 to the power of 2 and get 16.

$$sort(1,-192,\frac{16\times 5-\frac{8^{2}}{4}}{2}-\frac{5^{2}\times 2+3\times 5-2}{3})$$

Multiply 16 and 5 to get 80.

$$sort(1,-192,\frac{80-\frac{8^{2}}{4}}{2}-\frac{5^{2}\times 2+3\times 5-2}{3})$$

Calculate 8 to the power of 2 and get 64.

$$sort(1,-192,\frac{80-\frac{64}{4}}{2}-\frac{5^{2}\times 2+3\times 5-2}{3})$$

Divide 64 by 4 to get 16.

$$sort(1,-192,\frac{80-16}{2}-\frac{5^{2}\times 2+3\times 5-2}{3})$$

Subtract 16 from 80 to get 64.

$$sort(1,-192,\frac{64}{2}-\frac{5^{2}\times 2+3\times 5-2}{3})$$

Divide 64 by 2 to get 32.

$$sort(1,-192,32-\frac{5^{2}\times 2+3\times 5-2}{3})$$

Calculate 5 to the power of 2 and get 25.

$$sort(1,-192,32-\frac{25\times 2+3\times 5-2}{3})$$

Multiply 25 and 2 to get 50.

$$sort(1,-192,32-\frac{50+3\times 5-2}{3})$$

Multiply 3 and 5 to get 15.

$$sort(1,-192,32-\frac{50+15-2}{3})$$

Add 50 and 15 to get 65.

$$sort(1,-192,32-\frac{65-2}{3})$$

Subtract 2 from 65 to get 63.

$$sort(1,-192,32-\frac{63}{3})$$

Divide 63 by 3 to get 21.

$$sort(1,-192,32-21)$$

Subtract 21 from 32 to get 11.

$$sort(1,-192,11)$$

To sort the list, start from a single element 1.

$$1$$

Insert -192 to the appropriate location in the new list.

$$-192,1$$

Insert 11 to the appropriate location in the new list.

$$-192,1,11$$

Evaluate

$$1,\ -192,\ 11$$