Solve {l}{8+5^{4}-3^{2}*2^{2}-4^{3}+10-7^{3}-13^{2}-4^{2}}{13^{2}-3*5^{2}*2+3^{3}+6^{3}-5^{3}-2^{4}-11^{2}}{9^{3}*3-3^{2}*2-30^2:9-5^3*3^2-29^2}

$$\left. \begin{array} { l } { 8 + 5 ^ { 4 } - 3 ^ { 2 } \times 2 ^ { 2 } - 4 ^ { 3 } + 10 - 7 ^ { 3 } - 13 ^ { 2 } - 4 ^ { 2 } } \\ { 13 ^ { 2 } - 3 \times 5 ^ { 2 } \times 2 + 3 ^ { 3 } + 6 ^ { 3 } - 5 ^ { 3 } - 2 ^ { 4 } - 11 ^ { 2 } } \\ { 9 ^ { 3 } \times 3 - 3 ^ { 2 } \times 2 - 30 ^ { 2 } : 9 - 5 ^ { 3 } \times 3 ^ { 2 } - 29 ^ { 2 } } \end{array} \right.$$

Sort

$$0,15,103$$

Solution Steps

Calculate 5 to the power of 4 and get 625.

$$sort(8+625-3^{2}\times 2^{2}-4^{3}+10-7^{3}-13^{2}-4^{2},13^{2}-3\times 5^{2}\times 2+3^{3}+6^{3}-5^{3}-2^{4}-11^{2},9^{3}\times 3-3^{2}\times 2-\frac{30^{2}}{9}-5^{3}\times 3^{2}-29^{2})$$

Add 8 and 625 to get 633.

$$sort(633-3^{2}\times 2^{2}-4^{3}+10-7^{3}-13^{2}-4^{2},13^{2}-3\times 5^{2}\times 2+3^{3}+6^{3}-5^{3}-2^{4}-11^{2},9^{3}\times 3-3^{2}\times 2-\frac{30^{2}}{9}-5^{3}\times 3^{2}-29^{2})$$

Calculate 3 to the power of 2 and get 9.

$$sort(633-9\times 2^{2}-4^{3}+10-7^{3}-13^{2}-4^{2},13^{2}-3\times 5^{2}\times 2+3^{3}+6^{3}-5^{3}-2^{4}-11^{2},9^{3}\times 3-3^{2}\times 2-\frac{30^{2}}{9}-5^{3}\times 3^{2}-29^{2})$$

Calculate 2 to the power of 2 and get 4.

$$sort(633-9\times 4-4^{3}+10-7^{3}-13^{2}-4^{2},13^{2}-3\times 5^{2}\times 2+3^{3}+6^{3}-5^{3}-2^{4}-11^{2},9^{3}\times 3-3^{2}\times 2-\frac{30^{2}}{9}-5^{3}\times 3^{2}-29^{2})$$

Multiply 9 and 4 to get 36.

$$sort(633-36-4^{3}+10-7^{3}-13^{2}-4^{2},13^{2}-3\times 5^{2}\times 2+3^{3}+6^{3}-5^{3}-2^{4}-11^{2},9^{3}\times 3-3^{2}\times 2-\frac{30^{2}}{9}-5^{3}\times 3^{2}-29^{2})$$

Subtract 36 from 633 to get 597.

$$sort(597-4^{3}+10-7^{3}-13^{2}-4^{2},13^{2}-3\times 5^{2}\times 2+3^{3}+6^{3}-5^{3}-2^{4}-11^{2},9^{3}\times 3-3^{2}\times 2-\frac{30^{2}}{9}-5^{3}\times 3^{2}-29^{2})$$

Calculate 4 to the power of 3 and get 64.

$$sort(597-64+10-7^{3}-13^{2}-4^{2},13^{2}-3\times 5^{2}\times 2+3^{3}+6^{3}-5^{3}-2^{4}-11^{2},9^{3}\times 3-3^{2}\times 2-\frac{30^{2}}{9}-5^{3}\times 3^{2}-29^{2})$$

Subtract 64 from 597 to get 533.

$$sort(533+10-7^{3}-13^{2}-4^{2},13^{2}-3\times 5^{2}\times 2+3^{3}+6^{3}-5^{3}-2^{4}-11^{2},9^{3}\times 3-3^{2}\times 2-\frac{30^{2}}{9}-5^{3}\times 3^{2}-29^{2})$$

Add 533 and 10 to get 543.

$$sort(543-7^{3}-13^{2}-4^{2},13^{2}-3\times 5^{2}\times 2+3^{3}+6^{3}-5^{3}-2^{4}-11^{2},9^{3}\times 3-3^{2}\times 2-\frac{30^{2}}{9}-5^{3}\times 3^{2}-29^{2})$$

Calculate 7 to the power of 3 and get 343.

$$sort(543-343-13^{2}-4^{2},13^{2}-3\times 5^{2}\times 2+3^{3}+6^{3}-5^{3}-2^{4}-11^{2},9^{3}\times 3-3^{2}\times 2-\frac{30^{2}}{9}-5^{3}\times 3^{2}-29^{2})$$

Subtract 343 from 543 to get 200.

$$sort(200-13^{2}-4^{2},13^{2}-3\times 5^{2}\times 2+3^{3}+6^{3}-5^{3}-2^{4}-11^{2},9^{3}\times 3-3^{2}\times 2-\frac{30^{2}}{9}-5^{3}\times 3^{2}-29^{2})$$

Calculate 13 to the power of 2 and get 169.

$$sort(200-169-4^{2},13^{2}-3\times 5^{2}\times 2+3^{3}+6^{3}-5^{3}-2^{4}-11^{2},9^{3}\times 3-3^{2}\times 2-\frac{30^{2}}{9}-5^{3}\times 3^{2}-29^{2})$$

Subtract 169 from 200 to get 31.

$$sort(31-4^{2},13^{2}-3\times 5^{2}\times 2+3^{3}+6^{3}-5^{3}-2^{4}-11^{2},9^{3}\times 3-3^{2}\times 2-\frac{30^{2}}{9}-5^{3}\times 3^{2}-29^{2})$$

Calculate 4 to the power of 2 and get 16.

$$sort(31-16,13^{2}-3\times 5^{2}\times 2+3^{3}+6^{3}-5^{3}-2^{4}-11^{2},9^{3}\times 3-3^{2}\times 2-\frac{30^{2}}{9}-5^{3}\times 3^{2}-29^{2})$$

Subtract 16 from 31 to get 15.

$$sort(15,13^{2}-3\times 5^{2}\times 2+3^{3}+6^{3}-5^{3}-2^{4}-11^{2},9^{3}\times 3-3^{2}\times 2-\frac{30^{2}}{9}-5^{3}\times 3^{2}-29^{2})$$

Calculate 13 to the power of 2 and get 169.

$$sort(15,169-3\times 5^{2}\times 2+3^{3}+6^{3}-5^{3}-2^{4}-11^{2},9^{3}\times 3-3^{2}\times 2-\frac{30^{2}}{9}-5^{3}\times 3^{2}-29^{2})$$

Calculate 5 to the power of 2 and get 25.

$$sort(15,169-3\times 25\times 2+3^{3}+6^{3}-5^{3}-2^{4}-11^{2},9^{3}\times 3-3^{2}\times 2-\frac{30^{2}}{9}-5^{3}\times 3^{2}-29^{2})$$

Multiply 3 and 25 to get 75.

$$sort(15,169-75\times 2+3^{3}+6^{3}-5^{3}-2^{4}-11^{2},9^{3}\times 3-3^{2}\times 2-\frac{30^{2}}{9}-5^{3}\times 3^{2}-29^{2})$$

Multiply 75 and 2 to get 150.

$$sort(15,169-150+3^{3}+6^{3}-5^{3}-2^{4}-11^{2},9^{3}\times 3-3^{2}\times 2-\frac{30^{2}}{9}-5^{3}\times 3^{2}-29^{2})$$

Subtract 150 from 169 to get 19.

$$sort(15,19+3^{3}+6^{3}-5^{3}-2^{4}-11^{2},9^{3}\times 3-3^{2}\times 2-\frac{30^{2}}{9}-5^{3}\times 3^{2}-29^{2})$$

Calculate 3 to the power of 3 and get 27.

$$sort(15,19+27+6^{3}-5^{3}-2^{4}-11^{2},9^{3}\times 3-3^{2}\times 2-\frac{30^{2}}{9}-5^{3}\times 3^{2}-29^{2})$$

Add 19 and 27 to get 46.

$$sort(15,46+6^{3}-5^{3}-2^{4}-11^{2},9^{3}\times 3-3^{2}\times 2-\frac{30^{2}}{9}-5^{3}\times 3^{2}-29^{2})$$

Calculate 6 to the power of 3 and get 216.

$$sort(15,46+216-5^{3}-2^{4}-11^{2},9^{3}\times 3-3^{2}\times 2-\frac{30^{2}}{9}-5^{3}\times 3^{2}-29^{2})$$

Add 46 and 216 to get 262.

$$sort(15,262-5^{3}-2^{4}-11^{2},9^{3}\times 3-3^{2}\times 2-\frac{30^{2}}{9}-5^{3}\times 3^{2}-29^{2})$$

Calculate 5 to the power of 3 and get 125.

$$sort(15,262-125-2^{4}-11^{2},9^{3}\times 3-3^{2}\times 2-\frac{30^{2}}{9}-5^{3}\times 3^{2}-29^{2})$$

Subtract 125 from 262 to get 137.

$$sort(15,137-2^{4}-11^{2},9^{3}\times 3-3^{2}\times 2-\frac{30^{2}}{9}-5^{3}\times 3^{2}-29^{2})$$

Calculate 2 to the power of 4 and get 16.

$$sort(15,137-16-11^{2},9^{3}\times 3-3^{2}\times 2-\frac{30^{2}}{9}-5^{3}\times 3^{2}-29^{2})$$

Subtract 16 from 137 to get 121.

$$sort(15,121-11^{2},9^{3}\times 3-3^{2}\times 2-\frac{30^{2}}{9}-5^{3}\times 3^{2}-29^{2})$$

Calculate 11 to the power of 2 and get 121.

$$sort(15,121-121,9^{3}\times 3-3^{2}\times 2-\frac{30^{2}}{9}-5^{3}\times 3^{2}-29^{2})$$

Subtract 121 from 121 to get 0.

$$sort(15,0,9^{3}\times 3-3^{2}\times 2-\frac{30^{2}}{9}-5^{3}\times 3^{2}-29^{2})$$

Calculate 9 to the power of 3 and get 729.

$$sort(15,0,729\times 3-3^{2}\times 2-\frac{30^{2}}{9}-5^{3}\times 3^{2}-29^{2})$$

Multiply 729 and 3 to get 2187.

$$sort(15,0,2187-3^{2}\times 2-\frac{30^{2}}{9}-5^{3}\times 3^{2}-29^{2})$$

Calculate 3 to the power of 2 and get 9.

$$sort(15,0,2187-9\times 2-\frac{30^{2}}{9}-5^{3}\times 3^{2}-29^{2})$$

Multiply 9 and 2 to get 18.

$$sort(15,0,2187-18-\frac{30^{2}}{9}-5^{3}\times 3^{2}-29^{2})$$

Subtract 18 from 2187 to get 2169.

$$sort(15,0,2169-\frac{30^{2}}{9}-5^{3}\times 3^{2}-29^{2})$$

Calculate 30 to the power of 2 and get 900.

$$sort(15,0,2169-\frac{900}{9}-5^{3}\times 3^{2}-29^{2})$$

Divide 900 by 9 to get 100.

$$sort(15,0,2169-100-5^{3}\times 3^{2}-29^{2})$$

Subtract 100 from 2169 to get 2069.

$$sort(15,0,2069-5^{3}\times 3^{2}-29^{2})$$

Calculate 5 to the power of 3 and get 125.

$$sort(15,0,2069-125\times 3^{2}-29^{2})$$

Calculate 3 to the power of 2 and get 9.

$$sort(15,0,2069-125\times 9-29^{2})$$

Multiply 125 and 9 to get 1125.

$$sort(15,0,2069-1125-29^{2})$$

Subtract 1125 from 2069 to get 944.

$$sort(15,0,944-29^{2})$$

Calculate 29 to the power of 2 and get 841.

$$sort(15,0,944-841)$$

Subtract 841 from 944 to get 103.

$$sort(15,0,103)$$

To sort the list, start from a single element 15.

$$15$$

Insert 0 to the appropriate location in the new list.

$$0,15$$

Insert 103 to the appropriate location in the new list.

$$0,15,103$$

Evaluate

$$15,\ 0,\ 103$$