Solve {l}{3^{4}+2^{3}-6+12-5^{2}-8^{2}}{2^{2}*3^{2}-5^{2}+1^{4}}{4^{2}*4^{2}-4^{2}*3^{2}-2^{4}*2^{2}-5*2^{3}}{5^{2}*5^{3}-5^{7}:5^{3}-5^{2}*10^{2}}{15^{2}:5^{2}+2^{3}-2*5}{21-2*6+8^{2}-7^{2}+2^{4}*2-38-4^{2}}{2^3+5*3+4^3-3^4+6*7-6^2}

$$\left. \begin{array} { l } { 3 ^ { 4 } + 2 ^ { 3 } - 6 + 12 - 5 ^ { 2 } - 8 ^ { 2 } } \\ { 2 ^ { 2 } \times 3 ^ { 2 } - 5 ^ { 2 } + 1 ^ { 4 } } \\ { 4 ^ { 2 } \times 4 ^ { 2 } - 4 ^ { 2 } \times 3 ^ { 2 } - 2 ^ { 4 } \times 2 ^ { 2 } - 5 \times 2 ^ { 3 } } \\ { 5 ^ { 2 } \times 5 ^ { 3 } - 5 ^ { 7 } : 5 ^ { 3 } - 5 ^ { 2 } \times 10 ^ { 2 } } \\ { 15 ^ { 2 } : 5 ^ { 2 } + 2 ^ { 3 } - 2 \times 5 } \\ { 21 - 2 \times 6 + 8 ^ { 2 } - 7 ^ { 2 } + 2 ^ { 4 } \times 2 - 38 - 4 ^ { 2 } } \\ { 2 ^ { 3 } + 5 \times 3 + 4 ^ { 3 } - 3 ^ { 4 } + 6 \times 7 - 6 ^ { 2 } } \end{array} \right.$$

Sort

$$0,2,6,7,8,12,12$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 2 and 2 to get 4.

$$sort(3^{4}+2^{3}-6+12-5^{2}-8^{2},2^{2}\times 3^{2}-5^{2}+1^{4},4^{4}-4^{2}\times 3^{2}-2^{4}\times 2^{2}-5\times 2^{3},5^{2}\times 5^{3}-\frac{5^{7}}{5^{3}}-5^{2}\times 10^{2},\frac{15^{2}}{5^{2}}+2^{3}-2\times 5,21-2\times 6+8^{2}-7^{2}+2^{4}\times 2-38-4^{2},2^{3}+5\times 3+4^{3}-3^{4}+6\times 7-6^{2})$$

To multiply powers of the same base, add their exponents. Add 4 and 2 to get 6.

$$sort(3^{4}+2^{3}-6+12-5^{2}-8^{2},2^{2}\times 3^{2}-5^{2}+1^{4},4^{4}-4^{2}\times 3^{2}-2^{6}-5\times 2^{3},5^{2}\times 5^{3}-\frac{5^{7}}{5^{3}}-5^{2}\times 10^{2},\frac{15^{2}}{5^{2}}+2^{3}-2\times 5,21-2\times 6+8^{2}-7^{2}+2^{4}\times 2-38-4^{2},2^{3}+5\times 3+4^{3}-3^{4}+6\times 7-6^{2})$$

To multiply powers of the same base, add their exponents. Add 2 and 3 to get 5.

$$sort(3^{4}+2^{3}-6+12-5^{2}-8^{2},2^{2}\times 3^{2}-5^{2}+1^{4},4^{4}-4^{2}\times 3^{2}-2^{6}-5\times 2^{3},5^{5}-\frac{5^{7}}{5^{3}}-5^{2}\times 10^{2},\frac{15^{2}}{5^{2}}+2^{3}-2\times 5,21-2\times 6+8^{2}-7^{2}+2^{4}\times 2-38-4^{2},2^{3}+5\times 3+4^{3}-3^{4}+6\times 7-6^{2})$$

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent. Subtract 3 from 7 to get 4.

$$sort(3^{4}+2^{3}-6+12-5^{2}-8^{2},2^{2}\times 3^{2}-5^{2}+1^{4},4^{4}-4^{2}\times 3^{2}-2^{6}-5\times 2^{3},5^{5}-5^{4}-5^{2}\times 10^{2},\frac{15^{2}}{5^{2}}+2^{3}-2\times 5,21-2\times 6+8^{2}-7^{2}+2^{4}\times 2-38-4^{2},2^{3}+5\times 3+4^{3}-3^{4}+6\times 7-6^{2})$$

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

$$sort(3^{4}+2^{3}-6+12-5^{2}-8^{2},2^{2}\times 3^{2}-5^{2}+1^{4},4^{4}-4^{2}\times 3^{2}-2^{6}-5\times 2^{3},5^{5}-5^{4}-5^{2}\times 10^{2},\frac{15^{2}}{5^{2}}+2^{3}-2\times 5,21-2\times 6+8^{2}-7^{2}+2^{5}-38-4^{2},2^{3}+5\times 3+4^{3}-3^{4}+6\times 7-6^{2})$$

Calculate 3 to the power of 4 and get 81.

$$sort(81+2^{3}-6+12-5^{2}-8^{2},2^{2}\times 3^{2}-5^{2}+1^{4},4^{4}-4^{2}\times 3^{2}-2^{6}-5\times 2^{3},5^{5}-5^{4}-5^{2}\times 10^{2},\frac{15^{2}}{5^{2}}+2^{3}-2\times 5,21-2\times 6+8^{2}-7^{2}+2^{5}-38-4^{2},2^{3}+5\times 3+4^{3}-3^{4}+6\times 7-6^{2})$$

Calculate 2 to the power of 3 and get 8.

$$sort(81+8-6+12-5^{2}-8^{2},2^{2}\times 3^{2}-5^{2}+1^{4},4^{4}-4^{2}\times 3^{2}-2^{6}-5\times 2^{3},5^{5}-5^{4}-5^{2}\times 10^{2},\frac{15^{2}}{5^{2}}+2^{3}-2\times 5,21-2\times 6+8^{2}-7^{2}+2^{5}-38-4^{2},2^{3}+5\times 3+4^{3}-3^{4}+6\times 7-6^{2})$$

Add 81 and 8 to get 89.

$$sort(89-6+12-5^{2}-8^{2},2^{2}\times 3^{2}-5^{2}+1^{4},4^{4}-4^{2}\times 3^{2}-2^{6}-5\times 2^{3},5^{5}-5^{4}-5^{2}\times 10^{2},\frac{15^{2}}{5^{2}}+2^{3}-2\times 5,21-2\times 6+8^{2}-7^{2}+2^{5}-38-4^{2},2^{3}+5\times 3+4^{3}-3^{4}+6\times 7-6^{2})$$

Subtract 6 from 89 to get 83.

$$sort(83+12-5^{2}-8^{2},2^{2}\times 3^{2}-5^{2}+1^{4},4^{4}-4^{2}\times 3^{2}-2^{6}-5\times 2^{3},5^{5}-5^{4}-5^{2}\times 10^{2},\frac{15^{2}}{5^{2}}+2^{3}-2\times 5,21-2\times 6+8^{2}-7^{2}+2^{5}-38-4^{2},2^{3}+5\times 3+4^{3}-3^{4}+6\times 7-6^{2})$$

Add 83 and 12 to get 95.

$$sort(95-5^{2}-8^{2},2^{2}\times 3^{2}-5^{2}+1^{4},4^{4}-4^{2}\times 3^{2}-2^{6}-5\times 2^{3},5^{5}-5^{4}-5^{2}\times 10^{2},\frac{15^{2}}{5^{2}}+2^{3}-2\times 5,21-2\times 6+8^{2}-7^{2}+2^{5}-38-4^{2},2^{3}+5\times 3+4^{3}-3^{4}+6\times 7-6^{2})$$

Calculate 5 to the power of 2 and get 25.

$$sort(95-25-8^{2},2^{2}\times 3^{2}-5^{2}+1^{4},4^{4}-4^{2}\times 3^{2}-2^{6}-5\times 2^{3},5^{5}-5^{4}-5^{2}\times 10^{2},\frac{15^{2}}{5^{2}}+2^{3}-2\times 5,21-2\times 6+8^{2}-7^{2}+2^{5}-38-4^{2},2^{3}+5\times 3+4^{3}-3^{4}+6\times 7-6^{2})$$

Subtract 25 from 95 to get 70.

$$sort(70-8^{2},2^{2}\times 3^{2}-5^{2}+1^{4},4^{4}-4^{2}\times 3^{2}-2^{6}-5\times 2^{3},5^{5}-5^{4}-5^{2}\times 10^{2},\frac{15^{2}}{5^{2}}+2^{3}-2\times 5,21-2\times 6+8^{2}-7^{2}+2^{5}-38-4^{2},2^{3}+5\times 3+4^{3}-3^{4}+6\times 7-6^{2})$$

Calculate 8 to the power of 2 and get 64.

$$sort(70-64,2^{2}\times 3^{2}-5^{2}+1^{4},4^{4}-4^{2}\times 3^{2}-2^{6}-5\times 2^{3},5^{5}-5^{4}-5^{2}\times 10^{2},\frac{15^{2}}{5^{2}}+2^{3}-2\times 5,21-2\times 6+8^{2}-7^{2}+2^{5}-38-4^{2},2^{3}+5\times 3+4^{3}-3^{4}+6\times 7-6^{2})$$

Subtract 64 from 70 to get 6.

$$sort(6,2^{2}\times 3^{2}-5^{2}+1^{4},4^{4}-4^{2}\times 3^{2}-2^{6}-5\times 2^{3},5^{5}-5^{4}-5^{2}\times 10^{2},\frac{15^{2}}{5^{2}}+2^{3}-2\times 5,21-2\times 6+8^{2}-7^{2}+2^{5}-38-4^{2},2^{3}+5\times 3+4^{3}-3^{4}+6\times 7-6^{2})$$

Calculate 2 to the power of 2 and get 4.

$$sort(6,4\times 3^{2}-5^{2}+1^{4},4^{4}-4^{2}\times 3^{2}-2^{6}-5\times 2^{3},5^{5}-5^{4}-5^{2}\times 10^{2},\frac{15^{2}}{5^{2}}+2^{3}-2\times 5,21-2\times 6+8^{2}-7^{2}+2^{5}-38-4^{2},2^{3}+5\times 3+4^{3}-3^{4}+6\times 7-6^{2})$$

Calculate 3 to the power of 2 and get 9.

$$sort(6,4\times 9-5^{2}+1^{4},4^{4}-4^{2}\times 3^{2}-2^{6}-5\times 2^{3},5^{5}-5^{4}-5^{2}\times 10^{2},\frac{15^{2}}{5^{2}}+2^{3}-2\times 5,21-2\times 6+8^{2}-7^{2}+2^{5}-38-4^{2},2^{3}+5\times 3+4^{3}-3^{4}+6\times 7-6^{2})$$

Multiply 4 and 9 to get 36.

$$sort(6,36-5^{2}+1^{4},4^{4}-4^{2}\times 3^{2}-2^{6}-5\times 2^{3},5^{5}-5^{4}-5^{2}\times 10^{2},\frac{15^{2}}{5^{2}}+2^{3}-2\times 5,21-2\times 6+8^{2}-7^{2}+2^{5}-38-4^{2},2^{3}+5\times 3+4^{3}-3^{4}+6\times 7-6^{2})$$

Calculate 5 to the power of 2 and get 25.

$$sort(6,36-25+1^{4},4^{4}-4^{2}\times 3^{2}-2^{6}-5\times 2^{3},5^{5}-5^{4}-5^{2}\times 10^{2},\frac{15^{2}}{5^{2}}+2^{3}-2\times 5,21-2\times 6+8^{2}-7^{2}+2^{5}-38-4^{2},2^{3}+5\times 3+4^{3}-3^{4}+6\times 7-6^{2})$$

Subtract 25 from 36 to get 11.

$$sort(6,11+1^{4},4^{4}-4^{2}\times 3^{2}-2^{6}-5\times 2^{3},5^{5}-5^{4}-5^{2}\times 10^{2},\frac{15^{2}}{5^{2}}+2^{3}-2\times 5,21-2\times 6+8^{2}-7^{2}+2^{5}-38-4^{2},2^{3}+5\times 3+4^{3}-3^{4}+6\times 7-6^{2})$$

Calculate 1 to the power of 4 and get 1.

$$sort(6,11+1,4^{4}-4^{2}\times 3^{2}-2^{6}-5\times 2^{3},5^{5}-5^{4}-5^{2}\times 10^{2},\frac{15^{2}}{5^{2}}+2^{3}-2\times 5,21-2\times 6+8^{2}-7^{2}+2^{5}-38-4^{2},2^{3}+5\times 3+4^{3}-3^{4}+6\times 7-6^{2})$$

Add 11 and 1 to get 12.

$$sort(6,12,4^{4}-4^{2}\times 3^{2}-2^{6}-5\times 2^{3},5^{5}-5^{4}-5^{2}\times 10^{2},\frac{15^{2}}{5^{2}}+2^{3}-2\times 5,21-2\times 6+8^{2}-7^{2}+2^{5}-38-4^{2},2^{3}+5\times 3+4^{3}-3^{4}+6\times 7-6^{2})$$

Calculate 4 to the power of 4 and get 256.

$$sort(6,12,256-4^{2}\times 3^{2}-2^{6}-5\times 2^{3},5^{5}-5^{4}-5^{2}\times 10^{2},\frac{15^{2}}{5^{2}}+2^{3}-2\times 5,21-2\times 6+8^{2}-7^{2}+2^{5}-38-4^{2},2^{3}+5\times 3+4^{3}-3^{4}+6\times 7-6^{2})$$

Calculate 4 to the power of 2 and get 16.

$$sort(6,12,256-16\times 3^{2}-2^{6}-5\times 2^{3},5^{5}-5^{4}-5^{2}\times 10^{2},\frac{15^{2}}{5^{2}}+2^{3}-2\times 5,21-2\times 6+8^{2}-7^{2}+2^{5}-38-4^{2},2^{3}+5\times 3+4^{3}-3^{4}+6\times 7-6^{2})$$

Calculate 3 to the power of 2 and get 9.

$$sort(6,12,256-16\times 9-2^{6}-5\times 2^{3},5^{5}-5^{4}-5^{2}\times 10^{2},\frac{15^{2}}{5^{2}}+2^{3}-2\times 5,21-2\times 6+8^{2}-7^{2}+2^{5}-38-4^{2},2^{3}+5\times 3+4^{3}-3^{4}+6\times 7-6^{2})$$

Multiply 16 and 9 to get 144.

$$sort(6,12,256-144-2^{6}-5\times 2^{3},5^{5}-5^{4}-5^{2}\times 10^{2},\frac{15^{2}}{5^{2}}+2^{3}-2\times 5,21-2\times 6+8^{2}-7^{2}+2^{5}-38-4^{2},2^{3}+5\times 3+4^{3}-3^{4}+6\times 7-6^{2})$$

Subtract 144 from 256 to get 112.

$$sort(6,12,112-2^{6}-5\times 2^{3},5^{5}-5^{4}-5^{2}\times 10^{2},\frac{15^{2}}{5^{2}}+2^{3}-2\times 5,21-2\times 6+8^{2}-7^{2}+2^{5}-38-4^{2},2^{3}+5\times 3+4^{3}-3^{4}+6\times 7-6^{2})$$

Calculate 2 to the power of 6 and get 64.

$$sort(6,12,112-64-5\times 2^{3},5^{5}-5^{4}-5^{2}\times 10^{2},\frac{15^{2}}{5^{2}}+2^{3}-2\times 5,21-2\times 6+8^{2}-7^{2}+2^{5}-38-4^{2},2^{3}+5\times 3+4^{3}-3^{4}+6\times 7-6^{2})$$

Subtract 64 from 112 to get 48.

$$sort(6,12,48-5\times 2^{3},5^{5}-5^{4}-5^{2}\times 10^{2},\frac{15^{2}}{5^{2}}+2^{3}-2\times 5,21-2\times 6+8^{2}-7^{2}+2^{5}-38-4^{2},2^{3}+5\times 3+4^{3}-3^{4}+6\times 7-6^{2})$$

Calculate 2 to the power of 3 and get 8.

$$sort(6,12,48-5\times 8,5^{5}-5^{4}-5^{2}\times 10^{2},\frac{15^{2}}{5^{2}}+2^{3}-2\times 5,21-2\times 6+8^{2}-7^{2}+2^{5}-38-4^{2},2^{3}+5\times 3+4^{3}-3^{4}+6\times 7-6^{2})$$

Multiply 5 and 8 to get 40.

$$sort(6,12,48-40,5^{5}-5^{4}-5^{2}\times 10^{2},\frac{15^{2}}{5^{2}}+2^{3}-2\times 5,21-2\times 6+8^{2}-7^{2}+2^{5}-38-4^{2},2^{3}+5\times 3+4^{3}-3^{4}+6\times 7-6^{2})$$

Subtract 40 from 48 to get 8.

$$sort(6,12,8,5^{5}-5^{4}-5^{2}\times 10^{2},\frac{15^{2}}{5^{2}}+2^{3}-2\times 5,21-2\times 6+8^{2}-7^{2}+2^{5}-38-4^{2},2^{3}+5\times 3+4^{3}-3^{4}+6\times 7-6^{2})$$

Calculate 5 to the power of 5 and get 3125.

$$sort(6,12,8,3125-5^{4}-5^{2}\times 10^{2},\frac{15^{2}}{5^{2}}+2^{3}-2\times 5,21-2\times 6+8^{2}-7^{2}+2^{5}-38-4^{2},2^{3}+5\times 3+4^{3}-3^{4}+6\times 7-6^{2})$$

Calculate 5 to the power of 4 and get 625.

$$sort(6,12,8,3125-625-5^{2}\times 10^{2},\frac{15^{2}}{5^{2}}+2^{3}-2\times 5,21-2\times 6+8^{2}-7^{2}+2^{5}-38-4^{2},2^{3}+5\times 3+4^{3}-3^{4}+6\times 7-6^{2})$$

Subtract 625 from 3125 to get 2500.

$$sort(6,12,8,2500-5^{2}\times 10^{2},\frac{15^{2}}{5^{2}}+2^{3}-2\times 5,21-2\times 6+8^{2}-7^{2}+2^{5}-38-4^{2},2^{3}+5\times 3+4^{3}-3^{4}+6\times 7-6^{2})$$

Calculate 5 to the power of 2 and get 25.

$$sort(6,12,8,2500-25\times 10^{2},\frac{15^{2}}{5^{2}}+2^{3}-2\times 5,21-2\times 6+8^{2}-7^{2}+2^{5}-38-4^{2},2^{3}+5\times 3+4^{3}-3^{4}+6\times 7-6^{2})$$

Calculate 10 to the power of 2 and get 100.

$$sort(6,12,8,2500-25\times 100,\frac{15^{2}}{5^{2}}+2^{3}-2\times 5,21-2\times 6+8^{2}-7^{2}+2^{5}-38-4^{2},2^{3}+5\times 3+4^{3}-3^{4}+6\times 7-6^{2})$$

Multiply 25 and 100 to get 2500.

$$sort(6,12,8,2500-2500,\frac{15^{2}}{5^{2}}+2^{3}-2\times 5,21-2\times 6+8^{2}-7^{2}+2^{5}-38-4^{2},2^{3}+5\times 3+4^{3}-3^{4}+6\times 7-6^{2})$$

Subtract 2500 from 2500 to get 0.

$$sort(6,12,8,0,\frac{15^{2}}{5^{2}}+2^{3}-2\times 5,21-2\times 6+8^{2}-7^{2}+2^{5}-38-4^{2},2^{3}+5\times 3+4^{3}-3^{4}+6\times 7-6^{2})$$

Calculate 15 to the power of 2 and get 225.

$$sort(6,12,8,0,\frac{225}{5^{2}}+2^{3}-2\times 5,21-2\times 6+8^{2}-7^{2}+2^{5}-38-4^{2},2^{3}+5\times 3+4^{3}-3^{4}+6\times 7-6^{2})$$

Calculate 5 to the power of 2 and get 25.

$$sort(6,12,8,0,\frac{225}{25}+2^{3}-2\times 5,21-2\times 6+8^{2}-7^{2}+2^{5}-38-4^{2},2^{3}+5\times 3+4^{3}-3^{4}+6\times 7-6^{2})$$

Divide 225 by 25 to get 9.

$$sort(6,12,8,0,9+2^{3}-2\times 5,21-2\times 6+8^{2}-7^{2}+2^{5}-38-4^{2},2^{3}+5\times 3+4^{3}-3^{4}+6\times 7-6^{2})$$

Calculate 2 to the power of 3 and get 8.

$$sort(6,12,8,0,9+8-2\times 5,21-2\times 6+8^{2}-7^{2}+2^{5}-38-4^{2},2^{3}+5\times 3+4^{3}-3^{4}+6\times 7-6^{2})$$

Add 9 and 8 to get 17.

$$sort(6,12,8,0,17-2\times 5,21-2\times 6+8^{2}-7^{2}+2^{5}-38-4^{2},2^{3}+5\times 3+4^{3}-3^{4}+6\times 7-6^{2})$$

Multiply 2 and 5 to get 10.

$$sort(6,12,8,0,17-10,21-2\times 6+8^{2}-7^{2}+2^{5}-38-4^{2},2^{3}+5\times 3+4^{3}-3^{4}+6\times 7-6^{2})$$

Subtract 10 from 17 to get 7.

$$sort(6,12,8,0,7,21-2\times 6+8^{2}-7^{2}+2^{5}-38-4^{2},2^{3}+5\times 3+4^{3}-3^{4}+6\times 7-6^{2})$$

Multiply 2 and 6 to get 12.

$$sort(6,12,8,0,7,21-12+8^{2}-7^{2}+2^{5}-38-4^{2},2^{3}+5\times 3+4^{3}-3^{4}+6\times 7-6^{2})$$

Subtract 12 from 21 to get 9.

$$sort(6,12,8,0,7,9+8^{2}-7^{2}+2^{5}-38-4^{2},2^{3}+5\times 3+4^{3}-3^{4}+6\times 7-6^{2})$$

Calculate 8 to the power of 2 and get 64.

$$sort(6,12,8,0,7,9+64-7^{2}+2^{5}-38-4^{2},2^{3}+5\times 3+4^{3}-3^{4}+6\times 7-6^{2})$$

Add 9 and 64 to get 73.

$$sort(6,12,8,0,7,73-7^{2}+2^{5}-38-4^{2},2^{3}+5\times 3+4^{3}-3^{4}+6\times 7-6^{2})$$

Calculate 7 to the power of 2 and get 49.

$$sort(6,12,8,0,7,73-49+2^{5}-38-4^{2},2^{3}+5\times 3+4^{3}-3^{4}+6\times 7-6^{2})$$

Subtract 49 from 73 to get 24.

$$sort(6,12,8,0,7,24+2^{5}-38-4^{2},2^{3}+5\times 3+4^{3}-3^{4}+6\times 7-6^{2})$$

Calculate 2 to the power of 5 and get 32.

$$sort(6,12,8,0,7,24+32-38-4^{2},2^{3}+5\times 3+4^{3}-3^{4}+6\times 7-6^{2})$$

Add 24 and 32 to get 56.

$$sort(6,12,8,0,7,56-38-4^{2},2^{3}+5\times 3+4^{3}-3^{4}+6\times 7-6^{2})$$

Subtract 38 from 56 to get 18.

$$sort(6,12,8,0,7,18-4^{2},2^{3}+5\times 3+4^{3}-3^{4}+6\times 7-6^{2})$$

Calculate 4 to the power of 2 and get 16.

$$sort(6,12,8,0,7,18-16,2^{3}+5\times 3+4^{3}-3^{4}+6\times 7-6^{2})$$

Subtract 16 from 18 to get 2.

$$sort(6,12,8,0,7,2,2^{3}+5\times 3+4^{3}-3^{4}+6\times 7-6^{2})$$

Calculate 2 to the power of 3 and get 8.

$$sort(6,12,8,0,7,2,8+5\times 3+4^{3}-3^{4}+6\times 7-6^{2})$$

Multiply 5 and 3 to get 15.

$$sort(6,12,8,0,7,2,8+15+4^{3}-3^{4}+6\times 7-6^{2})$$

Add 8 and 15 to get 23.

$$sort(6,12,8,0,7,2,23+4^{3}-3^{4}+6\times 7-6^{2})$$

Calculate 4 to the power of 3 and get 64.

$$sort(6,12,8,0,7,2,23+64-3^{4}+6\times 7-6^{2})$$

Add 23 and 64 to get 87.

$$sort(6,12,8,0,7,2,87-3^{4}+6\times 7-6^{2})$$

Calculate 3 to the power of 4 and get 81.

$$sort(6,12,8,0,7,2,87-81+6\times 7-6^{2})$$

Subtract 81 from 87 to get 6.

$$sort(6,12,8,0,7,2,6+6\times 7-6^{2})$$

Multiply 6 and 7 to get 42.

$$sort(6,12,8,0,7,2,6+42-6^{2})$$

Add 6 and 42 to get 48.

$$sort(6,12,8,0,7,2,48-6^{2})$$

Calculate 6 to the power of 2 and get 36.

$$sort(6,12,8,0,7,2,48-36)$$

Subtract 36 from 48 to get 12.

$$sort(6,12,8,0,7,2,12)$$

To sort the list, start from a single element 6.

$$6$$

Insert 12 to the appropriate location in the new list.

$$6,12$$

Insert 8 to the appropriate location in the new list.

$$6,8,12$$

Insert 0 to the appropriate location in the new list.

$$0,6,8,12$$

Insert 7 to the appropriate location in the new list.

$$0,6,7,8,12$$

Insert 2 to the appropriate location in the new list.

$$0,2,6,7,8,12$$

Insert 12 to the appropriate location in the new list.

$$0,2,6,7,8,12,12$$

Evaluate

$$6,\ 12,\ 8,\ 0,\ 7,\ 2,\ 12$$