Solve {l}{5^1/45^-1/4}{27^-2/3}{27^-1/3}

$$\left. \begin{array} { l } { 5 ^ { 1 / 4 } 5 ^ { - 1 / 4 } } \\ { 27 ^ { - 2 / 3 } } \\ { 27 ^ { - 1 / 3 } } \end{array} \right.$$

Sort

$$\frac{1}{9},\frac{1}{3},1$$

Solution Steps

Multiply 5^{\frac{1}{4}} and 5^{-\frac{1}{4}} to get 1.

$$sort(1,27^{-\frac{2}{3}},27^{-\frac{1}{3}})$$

Calculate 27 to the power of -\frac{2}{3} and get \frac{1}{9}.

$$sort(1,\frac{1}{9},27^{-\frac{1}{3}})$$

Calculate 27 to the power of -\frac{1}{3} and get \frac{1}{3}.

$$sort(1,\frac{1}{9},\frac{1}{3})$$

Convert decimal numbers in the list 1,\frac{1}{9},\frac{1}{3} to fractions.

$$1,\frac{1}{9},\frac{1}{3}$$

Least common denominator of the numbers in the list 1,\frac{1}{9},\frac{1}{3} is 9. Convert numbers in the list to fractions with denominator 9.

$$\frac{9}{9},\frac{1}{9},\frac{3}{9}$$

To sort the list, start from a single element \frac{9}{9}.

$$\frac{9}{9}$$

Insert \frac{1}{9} to the appropriate location in the new list.

$$\frac{1}{9},\frac{9}{9}$$

Insert \frac{3}{9} to the appropriate location in the new list.

$$\frac{1}{9},\frac{3}{9},\frac{9}{9}$$

Replace the obtained fractions with the initial values.

$$\frac{1}{9},\frac{1}{3},1$$

Evaluate

$$1,\ \frac{1}{9},\ \frac{1}{3}$$