Solve {l}{frac{2^{2}+3^{5}}{3^{2}}}{1/2^{-3}-1/2^-3}{1^-3/2^9-1^-3/2}{}

$$\left. \begin{array} { l } { \frac { 2 ^ { 2 } + 3 ^ { 5 } } { 3 ^ { 2 } } } \\ { \frac { 1 } { 2 ^ { - 3 } } - \frac { 1 } { 2 ^ { - 3 } } } \\ { \frac { 1 ^ { - 3 } } { 2 ^ { 9 } } - \frac { 1 ^ { - 3 } } { 2 } } \\ { } \end{array} \right.$$

Sort

$$-\frac{255}{512},0,0,\frac{247}{9}$$

Solution Steps

Calculate 2 to the power of 2 and get 4.

$$sort(\frac{4+3^{5}}{3^{2}},\frac{1}{2^{-3}}-\frac{1}{2^{-3}},\frac{1^{-3}}{2^{9}}-\frac{1^{-3}}{2},0)$$

Calculate 3 to the power of 5 and get 243.

$$sort(\frac{4+243}{3^{2}},\frac{1}{2^{-3}}-\frac{1}{2^{-3}},\frac{1^{-3}}{2^{9}}-\frac{1^{-3}}{2},0)$$

Add 4 and 243 to get 247.

$$sort(\frac{247}{3^{2}},\frac{1}{2^{-3}}-\frac{1}{2^{-3}},\frac{1^{-3}}{2^{9}}-\frac{1^{-3}}{2},0)$$

Calculate 3 to the power of 2 and get 9.

$$sort(\frac{247}{9},\frac{1}{2^{-3}}-\frac{1}{2^{-3}},\frac{1^{-3}}{2^{9}}-\frac{1^{-3}}{2},0)$$

Calculate 2 to the power of -3 and get \frac{1}{8}.

$$sort(\frac{247}{9},\frac{1}{\frac{1}{8}}-\frac{1}{2^{-3}},\frac{1^{-3}}{2^{9}}-\frac{1^{-3}}{2},0)$$

Divide 1 by \frac{1}{8} by multiplying 1 by the reciprocal of \frac{1}{8}.

$$sort(\frac{247}{9},1\times 8-\frac{1}{2^{-3}},\frac{1^{-3}}{2^{9}}-\frac{1^{-3}}{2},0)$$

Multiply 1 and 8 to get 8.

$$sort(\frac{247}{9},8-\frac{1}{2^{-3}},\frac{1^{-3}}{2^{9}}-\frac{1^{-3}}{2},0)$$

Calculate 2 to the power of -3 and get \frac{1}{8}.

$$sort(\frac{247}{9},8-\frac{1}{\frac{1}{8}},\frac{1^{-3}}{2^{9}}-\frac{1^{-3}}{2},0)$$

Divide 1 by \frac{1}{8} by multiplying 1 by the reciprocal of \frac{1}{8}.

$$sort(\frac{247}{9},8-1\times 8,\frac{1^{-3}}{2^{9}}-\frac{1^{-3}}{2},0)$$

Multiply 1 and 8 to get 8.

$$sort(\frac{247}{9},8-8,\frac{1^{-3}}{2^{9}}-\frac{1^{-3}}{2},0)$$

Subtract 8 from 8 to get 0.

$$sort(\frac{247}{9},0,\frac{1^{-3}}{2^{9}}-\frac{1^{-3}}{2},0)$$

Calculate 1 to the power of -3 and get 1.

$$sort(\frac{247}{9},0,\frac{1}{2^{9}}-\frac{1^{-3}}{2},0)$$

Calculate 2 to the power of 9 and get 512.

$$sort(\frac{247}{9},0,\frac{1}{512}-\frac{1^{-3}}{2},0)$$

Calculate 1 to the power of -3 and get 1.

$$sort(\frac{247}{9},0,\frac{1}{512}-\frac{1}{2},0)$$

Subtract \frac{1}{2} from \frac{1}{512} to get -\frac{255}{512}.

$$sort(\frac{247}{9},0,-\frac{255}{512},0)$$

Convert decimal numbers in the list \frac{247}{9},0,-\frac{255}{512},0 to fractions.

$$\frac{247}{9},0,-\frac{255}{512},0$$

Least common denominator of the numbers in the list \frac{247}{9},0,-\frac{255}{512},0 is 4608. Convert numbers in the list to fractions with denominator 4608.

$$\frac{126464}{4608},0,-\frac{2295}{4608},0$$

To sort the list, start from a single element \frac{126464}{4608}.

$$\frac{126464}{4608}$$

Insert 0 to the appropriate location in the new list.

$$0,\frac{126464}{4608}$$

Insert -\frac{2295}{4608} to the appropriate location in the new list.

$$-\frac{2295}{4608},0,\frac{126464}{4608}$$

Insert 0 to the appropriate location in the new list.

$$-\frac{2295}{4608},0,0,\frac{126464}{4608}$$

Replace the obtained fractions with the initial values.

$$-\frac{255}{512},0,0,\frac{247}{9}$$

Evaluate

$$\frac{247}{9},\ 0,\ -\frac{255}{512},\ 0$$