Solve {l}{4}{-9^{2}}{3^{-2}}{6^{-3}}{(-5)^{2}}{(0,02)^{2}}{(0,1)^-5}{(-5)^-3}{(1/4)^2}{(3/2)^-3}

$$\left. \begin{array} { l } { 4 } \\ { - 9 ^ { 2 } } \\ { 3 ^ { - 2 } } \\ { 6 ^ { - 3 } } \\ { ( - 5 ) ^ { 2 } } \\ { ( 0,02 ) ^ { 2 } } \\ { ( 0,1 ) ^ { - 5 } } \\ { ( - 5 ) ^ { - 3 } } \\ { ( \frac { 1 } { 4 } ) ^ { 2 } } \\ { ( \frac { 3 } { 2 } ) ^ { - 3 } } \end{array} \right.$$

Sort

$$-81;-0,008;0,0004;\frac{1}{216};0,0625;\frac{1}{9};\frac{8}{27};4;25;100000$$

Solution Steps

Calculate 9 to the power of 2 and get 81.

$$sort(4;-81;3^{-2};6^{-3};\left(-5\right)^{2};0,02^{2};0,1^{-5};\left(-5\right)^{-3};\left(\frac{1}{4}\right)^{2};\left(\frac{3}{2}\right)^{-3})$$

Calculate 3 to the power of -2 and get \frac{1}{9}.

$$sort(4;-81;\frac{1}{9};6^{-3};\left(-5\right)^{2};0,02^{2};0,1^{-5};\left(-5\right)^{-3};\left(\frac{1}{4}\right)^{2};\left(\frac{3}{2}\right)^{-3})$$

Calculate 6 to the power of -3 and get \frac{1}{216}.

$$sort(4;-81;\frac{1}{9};\frac{1}{216};\left(-5\right)^{2};0,02^{2};0,1^{-5};\left(-5\right)^{-3};\left(\frac{1}{4}\right)^{2};\left(\frac{3}{2}\right)^{-3})$$

Calculate -5 to the power of 2 and get 25.

$$sort(4;-81;\frac{1}{9};\frac{1}{216};25;0,02^{2};0,1^{-5};\left(-5\right)^{-3};\left(\frac{1}{4}\right)^{2};\left(\frac{3}{2}\right)^{-3})$$

Calculate 0,02 to the power of 2 and get 0,0004.

$$sort(4;-81;\frac{1}{9};\frac{1}{216};25;0,0004;0,1^{-5};\left(-5\right)^{-3};\left(\frac{1}{4}\right)^{2};\left(\frac{3}{2}\right)^{-3})$$

Calculate 0,1 to the power of -5 and get 100000.

$$sort(4;-81;\frac{1}{9};\frac{1}{216};25;0,0004;100000;\left(-5\right)^{-3};\left(\frac{1}{4}\right)^{2};\left(\frac{3}{2}\right)^{-3})$$

Calculate -5 to the power of -3 and get -\frac{1}{125}.

$$sort(4;-81;\frac{1}{9};\frac{1}{216};25;0,0004;100000;-\frac{1}{125};\left(\frac{1}{4}\right)^{2};\left(\frac{3}{2}\right)^{-3})$$

Calculate \frac{1}{4} to the power of 2 and get \frac{1}{16}.

$$sort(4;-81;\frac{1}{9};\frac{1}{216};25;0,0004;100000;-\frac{1}{125};\frac{1}{16};\left(\frac{3}{2}\right)^{-3})$$

Calculate \frac{3}{2} to the power of -3 and get \frac{8}{27}.

$$sort(4;-81;\frac{1}{9};\frac{1}{216};25;0,0004;100000;-\frac{1}{125};\frac{1}{16};\frac{8}{27})$$

Convert decimal numbers in the list 4;-81;\frac{1}{9};\frac{1}{216};25;0,0004;100000;-\frac{1}{125};\frac{1}{16};\frac{8}{27} to fractions.

$$4;-81;\frac{1}{9};\frac{1}{216};25;\frac{1}{2500};100000;-\frac{1}{125};\frac{1}{16};\frac{8}{27}$$

Least common denominator of the numbers in the list 4;-81;\frac{1}{9};\frac{1}{216};25;\frac{1}{2500};100000;-\frac{1}{125};\frac{1}{16};\frac{8}{27} is 270000. Convert numbers in the list to fractions with denominator 270000.

$$\frac{1080000}{270000};-\frac{21870000}{270000};\frac{30000}{270000};\frac{1250}{270000};\frac{6750000}{270000};\frac{108}{270000};\frac{27000000000}{270000};-\frac{2160}{270000};\frac{16875}{270000};\frac{80000}{270000}$$

To sort the list, start from a single element \frac{1080000}{270000}.

$$\frac{1080000}{270000}$$

Insert -\frac{21870000}{270000} to the appropriate location in the new list.

$$-\frac{21870000}{270000};\frac{1080000}{270000}$$

Insert \frac{30000}{270000} to the appropriate location in the new list.

$$-\frac{21870000}{270000};\frac{30000}{270000};\frac{1080000}{270000}$$

Insert \frac{1250}{270000} to the appropriate location in the new list.

$$-\frac{21870000}{270000};\frac{1250}{270000};\frac{30000}{270000};\frac{1080000}{270000}$$

Insert \frac{6750000}{270000} to the appropriate location in the new list.

$$-\frac{21870000}{270000};\frac{1250}{270000};\frac{30000}{270000};\frac{1080000}{270000};\frac{6750000}{270000}$$

Insert \frac{108}{270000} to the appropriate location in the new list.

$$-\frac{21870000}{270000};\frac{108}{270000};\frac{1250}{270000};\frac{30000}{270000};\frac{1080000}{270000};\frac{6750000}{270000}$$

Insert \frac{27000000000}{270000} to the appropriate location in the new list.

$$-\frac{21870000}{270000};\frac{108}{270000};\frac{1250}{270000};\frac{30000}{270000};\frac{1080000}{270000};\frac{6750000}{270000};\frac{27000000000}{270000}$$

Insert -\frac{2160}{270000} to the appropriate location in the new list.

$$-\frac{21870000}{270000};-\frac{2160}{270000};\frac{108}{270000};\frac{1250}{270000};\frac{30000}{270000};\frac{1080000}{270000};\frac{6750000}{270000};\frac{27000000000}{270000}$$

Insert \frac{16875}{270000} to the appropriate location in the new list.

$$-\frac{21870000}{270000};-\frac{2160}{270000};\frac{108}{270000};\frac{1250}{270000};\frac{16875}{270000};\frac{30000}{270000};\frac{1080000}{270000};\frac{6750000}{270000};\frac{27000000000}{270000}$$

Insert \frac{80000}{270000} to the appropriate location in the new list.

$$-\frac{21870000}{270000};-\frac{2160}{270000};\frac{108}{270000};\frac{1250}{270000};\frac{16875}{270000};\frac{30000}{270000};\frac{80000}{270000};\frac{1080000}{270000};\frac{6750000}{270000};\frac{27000000000}{270000}$$

Replace the obtained fractions with the initial values.

$$-81;-\frac{1}{125};0,0004;\frac{1}{216};\frac{1}{16};\frac{1}{9};\frac{8}{27};4;25;100000$$

Evaluate

$$4,\ -81,\ \frac{1}{9},\ \frac{1}{216},\ 25,\ 0,0004,\ 100000,\ -0,008,\ 0,0625,\ \frac{8}{27}$$