Solve {l}{5*10^{3}+7*10^{2}+1*10^{1}+4}{6*10^{4}+3*10^{3}+1*10^{2}+8*10^{1}+5}{8*10^{5}+0*10^4+7*10^3+3*10^2+5*10^1+6}

$$\left. \begin{array} { l } { 5 \times 10 ^ { 3 } + 7 \times 10 ^ { 2 } + 1 \times 10 ^ { 1 } + 4 } \\ { 6 \times 10 ^ { 4 } + 3 \times 10 ^ { 3 } + 1 \times 10 ^ { 2 } + 8 \times 10 ^ { 1 } + 5 } \\ { 8 \times 10 ^ { 5 } + 0 \times 10 ^ { 4 } + 7 \times 10 ^ { 3 } + 3 \times 10 ^ { 2 } + 5 \times 10 ^ { 1 } + 6 } \end{array} \right.$$

Sort

$$5714,\ 63185,\ 807356$$

Solution Steps

Calculate 10 to the power of 3 and get 1000.

$$sort(5\times 1000+7\times 10^{2}+1\times 10^{1}+4,6\times 10^{4}+3\times 10^{3}+1\times 10^{2}+8\times 10^{1}+5,8\times 10^{5}+0\times 10^{4}+7\times 10^{3}+3\times 10^{2}+5\times 10^{1}+6)$$

Multiply 5 and 1000 to get 5000.

$$sort(5000+7\times 10^{2}+1\times 10^{1}+4,6\times 10^{4}+3\times 10^{3}+1\times 10^{2}+8\times 10^{1}+5,8\times 10^{5}+0\times 10^{4}+7\times 10^{3}+3\times 10^{2}+5\times 10^{1}+6)$$

Calculate 10 to the power of 2 and get 100.

$$sort(5000+7\times 100+1\times 10^{1}+4,6\times 10^{4}+3\times 10^{3}+1\times 10^{2}+8\times 10^{1}+5,8\times 10^{5}+0\times 10^{4}+7\times 10^{3}+3\times 10^{2}+5\times 10^{1}+6)$$

Multiply 7 and 100 to get 700.

$$sort(5000+700+1\times 10^{1}+4,6\times 10^{4}+3\times 10^{3}+1\times 10^{2}+8\times 10^{1}+5,8\times 10^{5}+0\times 10^{4}+7\times 10^{3}+3\times 10^{2}+5\times 10^{1}+6)$$

Add 5000 and 700 to get 5700.

$$sort(5700+1\times 10^{1}+4,6\times 10^{4}+3\times 10^{3}+1\times 10^{2}+8\times 10^{1}+5,8\times 10^{5}+0\times 10^{4}+7\times 10^{3}+3\times 10^{2}+5\times 10^{1}+6)$$

Calculate 10 to the power of 1 and get 10.

$$sort(5700+1\times 10+4,6\times 10^{4}+3\times 10^{3}+1\times 10^{2}+8\times 10^{1}+5,8\times 10^{5}+0\times 10^{4}+7\times 10^{3}+3\times 10^{2}+5\times 10^{1}+6)$$

Multiply 1 and 10 to get 10.

$$sort(5700+10+4,6\times 10^{4}+3\times 10^{3}+1\times 10^{2}+8\times 10^{1}+5,8\times 10^{5}+0\times 10^{4}+7\times 10^{3}+3\times 10^{2}+5\times 10^{1}+6)$$

Add 5700 and 10 to get 5710.

$$sort(5710+4,6\times 10^{4}+3\times 10^{3}+1\times 10^{2}+8\times 10^{1}+5,8\times 10^{5}+0\times 10^{4}+7\times 10^{3}+3\times 10^{2}+5\times 10^{1}+6)$$

Add 5710 and 4 to get 5714.

$$sort(5714,6\times 10^{4}+3\times 10^{3}+1\times 10^{2}+8\times 10^{1}+5,8\times 10^{5}+0\times 10^{4}+7\times 10^{3}+3\times 10^{2}+5\times 10^{1}+6)$$

Calculate 10 to the power of 4 and get 10000.

$$sort(5714,6\times 10000+3\times 10^{3}+1\times 10^{2}+8\times 10^{1}+5,8\times 10^{5}+0\times 10^{4}+7\times 10^{3}+3\times 10^{2}+5\times 10^{1}+6)$$

Multiply 6 and 10000 to get 60000.

$$sort(5714,60000+3\times 10^{3}+1\times 10^{2}+8\times 10^{1}+5,8\times 10^{5}+0\times 10^{4}+7\times 10^{3}+3\times 10^{2}+5\times 10^{1}+6)$$

Calculate 10 to the power of 3 and get 1000.

$$sort(5714,60000+3\times 1000+1\times 10^{2}+8\times 10^{1}+5,8\times 10^{5}+0\times 10^{4}+7\times 10^{3}+3\times 10^{2}+5\times 10^{1}+6)$$

Multiply 3 and 1000 to get 3000.

$$sort(5714,60000+3000+1\times 10^{2}+8\times 10^{1}+5,8\times 10^{5}+0\times 10^{4}+7\times 10^{3}+3\times 10^{2}+5\times 10^{1}+6)$$

Add 60000 and 3000 to get 63000.

$$sort(5714,63000+1\times 10^{2}+8\times 10^{1}+5,8\times 10^{5}+0\times 10^{4}+7\times 10^{3}+3\times 10^{2}+5\times 10^{1}+6)$$

Calculate 10 to the power of 2 and get 100.

$$sort(5714,63000+1\times 100+8\times 10^{1}+5,8\times 10^{5}+0\times 10^{4}+7\times 10^{3}+3\times 10^{2}+5\times 10^{1}+6)$$

Multiply 1 and 100 to get 100.

$$sort(5714,63000+100+8\times 10^{1}+5,8\times 10^{5}+0\times 10^{4}+7\times 10^{3}+3\times 10^{2}+5\times 10^{1}+6)$$

Add 63000 and 100 to get 63100.

$$sort(5714,63100+8\times 10^{1}+5,8\times 10^{5}+0\times 10^{4}+7\times 10^{3}+3\times 10^{2}+5\times 10^{1}+6)$$

Calculate 10 to the power of 1 and get 10.

$$sort(5714,63100+8\times 10+5,8\times 10^{5}+0\times 10^{4}+7\times 10^{3}+3\times 10^{2}+5\times 10^{1}+6)$$

Multiply 8 and 10 to get 80.

$$sort(5714,63100+80+5,8\times 10^{5}+0\times 10^{4}+7\times 10^{3}+3\times 10^{2}+5\times 10^{1}+6)$$

Add 63100 and 80 to get 63180.

$$sort(5714,63180+5,8\times 10^{5}+0\times 10^{4}+7\times 10^{3}+3\times 10^{2}+5\times 10^{1}+6)$$

Add 63180 and 5 to get 63185.

$$sort(5714,63185,8\times 10^{5}+0\times 10^{4}+7\times 10^{3}+3\times 10^{2}+5\times 10^{1}+6)$$

Calculate 10 to the power of 5 and get 100000.

$$sort(5714,63185,8\times 100000+0\times 10^{4}+7\times 10^{3}+3\times 10^{2}+5\times 10^{1}+6)$$

Multiply 8 and 100000 to get 800000.

$$sort(5714,63185,800000+0\times 10^{4}+7\times 10^{3}+3\times 10^{2}+5\times 10^{1}+6)$$

Calculate 10 to the power of 4 and get 10000.

$$sort(5714,63185,800000+0\times 10000+7\times 10^{3}+3\times 10^{2}+5\times 10^{1}+6)$$

Multiply 0 and 10000 to get 0.

$$sort(5714,63185,800000+0+7\times 10^{3}+3\times 10^{2}+5\times 10^{1}+6)$$

Add 800000 and 0 to get 800000.

$$sort(5714,63185,800000+7\times 10^{3}+3\times 10^{2}+5\times 10^{1}+6)$$

Calculate 10 to the power of 3 and get 1000.

$$sort(5714,63185,800000+7\times 1000+3\times 10^{2}+5\times 10^{1}+6)$$

Multiply 7 and 1000 to get 7000.

$$sort(5714,63185,800000+7000+3\times 10^{2}+5\times 10^{1}+6)$$

Add 800000 and 7000 to get 807000.

$$sort(5714,63185,807000+3\times 10^{2}+5\times 10^{1}+6)$$

Calculate 10 to the power of 2 and get 100.

$$sort(5714,63185,807000+3\times 100+5\times 10^{1}+6)$$

Multiply 3 and 100 to get 300.

$$sort(5714,63185,807000+300+5\times 10^{1}+6)$$

Add 807000 and 300 to get 807300.

$$sort(5714,63185,807300+5\times 10^{1}+6)$$

Calculate 10 to the power of 1 and get 10.

$$sort(5714,63185,807300+5\times 10+6)$$

Multiply 5 and 10 to get 50.

$$sort(5714,63185,807300+50+6)$$

Add 807300 and 50 to get 807350.

$$sort(5714,63185,807350+6)$$

Add 807350 and 6 to get 807356.

$$sort(5714,63185,807356)$$

The list values are already in order.

$$5714,63185,807356$$

Evaluate

$$5714,\ 63185,\ 807356$$