Solve {c}{frac{2^{3}*3^{4}*4}{3*32}}{frac{3*7^{2}*11^{8}}{21*11^3}}{2^0*3^0*4^0}

$$\left. \begin{array} { c } { \frac { 2 ^ { 3 } \times 3 ^ { 4 } \times 4 } { 3 \times 32 } } \\ { \frac { 3 \times 7 ^ { 2 } \times 11 ^ { 8 } } { 21 \times 11 ^ { 3 } } } \\ { 2 ^ { 0 } \times 3 ^ { 0 } \times 4 ^ { 0 } } \end{array} \right.$$

Sort

$$1,27,1127357$$

Solution Steps

Cancel out 3\times 4 in both numerator and denominator.

$$sort(\frac{2^{3}\times 3^{3}}{8},\frac{3\times 7^{2}\times 11^{8}}{21\times 11^{3}},2^{0}\times 3^{0}\times 4^{0})$$

Calculate 2 to the power of 3 and get 8.

$$sort(\frac{8\times 3^{3}}{8},\frac{3\times 7^{2}\times 11^{8}}{21\times 11^{3}},2^{0}\times 3^{0}\times 4^{0})$$

Calculate 3 to the power of 3 and get 27.

$$sort(\frac{8\times 27}{8},\frac{3\times 7^{2}\times 11^{8}}{21\times 11^{3}},2^{0}\times 3^{0}\times 4^{0})$$

Multiply 8 and 27 to get 216.

$$sort(\frac{216}{8},\frac{3\times 7^{2}\times 11^{8}}{21\times 11^{3}},2^{0}\times 3^{0}\times 4^{0})$$

Divide 216 by 8 to get 27.

$$sort(27,\frac{3\times 7^{2}\times 11^{8}}{21\times 11^{3}},2^{0}\times 3^{0}\times 4^{0})$$

Cancel out 3\times 7\times 11^{3} in both numerator and denominator.

$$sort(27,7\times 11^{5},2^{0}\times 3^{0}\times 4^{0})$$

Calculate 2 to the power of 0 and get 1.

$$sort(27,7\times 11^{5},1\times 3^{0}\times 4^{0})$$

Calculate 3 to the power of 0 and get 1.

$$sort(27,7\times 11^{5},1\times 1\times 4^{0})$$

Multiply 1 and 1 to get 1.

$$sort(27,7\times 11^{5},4^{0})$$

Calculate 4 to the power of 0 and get 1.

$$sort(27,7\times 11^{5},1)$$

Calculate 11 to the power of 5 and get 161051.

$$sort(27,7\times 161051,1)$$

Multiply 7 and 161051 to get 1127357.

$$sort(27,1127357,1)$$

To sort the list, start from a single element 27.

$$27$$

Insert 1127357 to the appropriate location in the new list.

$$27,1127357$$

Insert 1 to the appropriate location in the new list.

$$1,27,1127357$$

Evaluate

$$27,\ 1127357,\ 1$$