Solve {l}{2^{2}*3^{2}-5^{2}+1^{4}}{4^{2}*4^{2}-4^{2}*3^2-2^4*2^2-5*2^3}

$$\left. \begin{array} { l } { 2 ^ { 2 } \times 3 ^ { 2 } - 5 ^ { 2 } + 1 ^ { 4 } } \\ { 4 ^ { 2 } \times 4 ^ { 2 } - 4 ^ { 2 } \times 3 ^ { 2 } - 2 ^ { 4 } \times 2 ^ { 2 } - 5 \times 2 ^ { 3 } } \end{array} \right.$$

Sort

$$8,12$$

Solution Steps

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

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

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

$$sort(2^{2}\times 3^{2}-5^{2}+1^{4},4^{4}-4^{2}\times 3^{2}-2^{6}-5\times 2^{3})$$

Calculate 2 to the power of 2 and get 4.

$$sort(4\times 3^{2}-5^{2}+1^{4},4^{4}-4^{2}\times 3^{2}-2^{6}-5\times 2^{3})$$

Calculate 3 to the power of 2 and get 9.

$$sort(4\times 9-5^{2}+1^{4},4^{4}-4^{2}\times 3^{2}-2^{6}-5\times 2^{3})$$

Multiply 4 and 9 to get 36.

$$sort(36-5^{2}+1^{4},4^{4}-4^{2}\times 3^{2}-2^{6}-5\times 2^{3})$$

Calculate 5 to the power of 2 and get 25.

$$sort(36-25+1^{4},4^{4}-4^{2}\times 3^{2}-2^{6}-5\times 2^{3})$$

Subtract 25 from 36 to get 11.

$$sort(11+1^{4},4^{4}-4^{2}\times 3^{2}-2^{6}-5\times 2^{3})$$

Calculate 1 to the power of 4 and get 1.

$$sort(11+1,4^{4}-4^{2}\times 3^{2}-2^{6}-5\times 2^{3})$$

Add 11 and 1 to get 12.

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

Calculate 4 to the power of 4 and get 256.

$$sort(12,256-4^{2}\times 3^{2}-2^{6}-5\times 2^{3})$$

Calculate 4 to the power of 2 and get 16.

$$sort(12,256-16\times 3^{2}-2^{6}-5\times 2^{3})$$

Calculate 3 to the power of 2 and get 9.

$$sort(12,256-16\times 9-2^{6}-5\times 2^{3})$$

Multiply 16 and 9 to get 144.

$$sort(12,256-144-2^{6}-5\times 2^{3})$$

Subtract 144 from 256 to get 112.

$$sort(12,112-2^{6}-5\times 2^{3})$$

Calculate 2 to the power of 6 and get 64.

$$sort(12,112-64-5\times 2^{3})$$

Subtract 64 from 112 to get 48.

$$sort(12,48-5\times 2^{3})$$

Calculate 2 to the power of 3 and get 8.

$$sort(12,48-5\times 8)$$

Multiply 5 and 8 to get 40.

$$sort(12,48-40)$$

Subtract 40 from 48 to get 8.

$$sort(12,8)$$

To sort the list, start from a single element 12.

$$12$$

Insert 8 to the appropriate location in the new list.

$$8,12$$

Evaluate

$$12,\ 8$$