Solve {l}{(frac{2(9)^frac{5{2}}}{5}-frac{8(9)^frac{3{2}}}{3})}{(frac{2(4)^frac{5{2}}}{5}-frac{8(4)^frac{3{2}}}{3})}

$$\left. \begin{array} { l } { ( \frac { 2 ( 9 ) ^ { \frac { 5 } { 2 } } } { 5 } - \frac { 8 ( 9 ) ^ { \frac { 3 } { 2 } } } { 3 } ) } \\ { ( \frac { 2 ( 4 ) ^ { \frac { 5 } { 2 } } } { 5 } - \frac { 8 ( 4 ) ^ { \frac { 3 } { 2 } } } { 3 } ) } \end{array} \right.$$

Sort

$$-\frac{128}{15},\frac{126}{5}$$

Solution Steps

Calculate 9 to the power of \frac{5}{2} and get 243.

$$sort(\frac{2\times 243}{5}-\frac{8\times 9^{\frac{3}{2}}}{3},\frac{2\times 4^{\frac{5}{2}}}{5}-\frac{8\times 4^{\frac{3}{2}}}{3})$$

Multiply 2 and 243 to get 486.

$$sort(\frac{486}{5}-\frac{8\times 9^{\frac{3}{2}}}{3},\frac{2\times 4^{\frac{5}{2}}}{5}-\frac{8\times 4^{\frac{3}{2}}}{3})$$

Calculate 9 to the power of \frac{3}{2} and get 27.

$$sort(\frac{486}{5}-\frac{8\times 27}{3},\frac{2\times 4^{\frac{5}{2}}}{5}-\frac{8\times 4^{\frac{3}{2}}}{3})$$

Multiply 8 and 27 to get 216.

$$sort(\frac{486}{5}-\frac{216}{3},\frac{2\times 4^{\frac{5}{2}}}{5}-\frac{8\times 4^{\frac{3}{2}}}{3})$$

Divide 216 by 3 to get 72.

$$sort(\frac{486}{5}-72,\frac{2\times 4^{\frac{5}{2}}}{5}-\frac{8\times 4^{\frac{3}{2}}}{3})$$

Subtract 72 from \frac{486}{5} to get \frac{126}{5}.

$$sort(\frac{126}{5},\frac{2\times 4^{\frac{5}{2}}}{5}-\frac{8\times 4^{\frac{3}{2}}}{3})$$

Calculate 4 to the power of \frac{5}{2} and get 32.

$$sort(\frac{126}{5},\frac{2\times 32}{5}-\frac{8\times 4^{\frac{3}{2}}}{3})$$

Multiply 2 and 32 to get 64.

$$sort(\frac{126}{5},\frac{64}{5}-\frac{8\times 4^{\frac{3}{2}}}{3})$$

Calculate 4 to the power of \frac{3}{2} and get 8.

$$sort(\frac{126}{5},\frac{64}{5}-\frac{8\times 8}{3})$$

Multiply 8 and 8 to get 64.

$$sort(\frac{126}{5},\frac{64}{5}-\frac{64}{3})$$

Subtract \frac{64}{3} from \frac{64}{5} to get -\frac{128}{15}.

$$sort(\frac{126}{5},-\frac{128}{15})$$

Least common denominator of the numbers in the list \frac{126}{5},-\frac{128}{15} is 15. Convert numbers in the list to fractions with denominator 15.

$$\frac{378}{15},-\frac{128}{15}$$

To sort the list, start from a single element \frac{378}{15}.

$$\frac{378}{15}$$

Insert -\frac{128}{15} to the appropriate location in the new list.

$$-\frac{128}{15},\frac{378}{15}$$

Replace the obtained fractions with the initial values.

$$-\frac{128}{15},\frac{126}{5}$$

Evaluate

$$\frac{126}{5},\ -\frac{128}{15}$$