Solve {l}{3^{2}4^{2}}{3^34^3}{3^44^4}{44}{88}{44}

$$\left. \begin{array} { l } { 3 ^ { 2 } 4 ^ { 2 } } \\ { 3 ^ { 3 } 4 ^ { 3 } } \\ { 3 ^ { 4 } 4 ^ { 4 } } \\ { 44 } \\ { 88 } \\ { 44 } \end{array} \right.$$

Sort

$$44,44,88,144,1728,20736$$

Solution Steps

Calculate 3 to the power of 2 and get 9.

$$sort(9\times 4^{2},3^{3}\times 4^{3},3^{4}\times 4^{4},44,88,44)$$

Calculate 4 to the power of 2 and get 16.

$$sort(9\times 16,3^{3}\times 4^{3},3^{4}\times 4^{4},44,88,44)$$

Multiply 9 and 16 to get 144.

$$sort(144,3^{3}\times 4^{3},3^{4}\times 4^{4},44,88,44)$$

Calculate 3 to the power of 3 and get 27.

$$sort(144,27\times 4^{3},3^{4}\times 4^{4},44,88,44)$$

Calculate 4 to the power of 3 and get 64.

$$sort(144,27\times 64,3^{4}\times 4^{4},44,88,44)$$

Multiply 27 and 64 to get 1728.

$$sort(144,1728,3^{4}\times 4^{4},44,88,44)$$

Calculate 3 to the power of 4 and get 81.

$$sort(144,1728,81\times 4^{4},44,88,44)$$

Calculate 4 to the power of 4 and get 256.

$$sort(144,1728,81\times 256,44,88,44)$$

Multiply 81 and 256 to get 20736.

$$sort(144,1728,20736,44,88,44)$$

To sort the list, start from a single element 144.

$$144$$

Insert 1728 to the appropriate location in the new list.

$$144,1728$$

Insert 20736 to the appropriate location in the new list.

$$144,1728,20736$$

Insert 44 to the appropriate location in the new list.

$$44,144,1728,20736$$

Insert 88 to the appropriate location in the new list.

$$44,88,144,1728,20736$$

Insert 44 to the appropriate location in the new list.

$$44,44,88,144,1728,20736$$

Evaluate

$$144,\ 1728,\ 20736,\ 44,\ 88,\ 44$$