Answer
$$\frac{1}{{\root a \of 2 }}$$
Work Step by Step
$$\eqalign{
& \frac{{{2^{1/a}}}}{{{2^{2/a}}}} \cr
& {\text{Use the exponent identity }}\frac{{{a^m}}}{{{a^n}}} = {a^{m - n}} \cr
& \frac{{{2^{1/a}}}}{{{2^{2/a}}}} = {2^{1/a - 2/a}} \cr
& \frac{{{2^{1/a}}}}{{{2^{2/a}}}} = {2^{\frac{{1 - 2}}{a}}} \cr
& {\text{Simplifying}} \cr
& \frac{{{2^{1/a}}}}{{{2^{2/a}}}} = {2^{ - \frac{1}{a}}} \cr
& {\text{Use negative integer exponent rule }}{a^{ - n}} = \frac{1}{{{a^n}}} \cr
& = \frac{1}{{{2^{1/a}}}} \cr
& {\text{Using radical properties}} \cr
& = \frac{1}{{\root a \of 2 }} \cr} $$
