We have the following rules that we need for this problem:
i) [tex]\displaystyle { a^{\frac{1}{2}}=\sqrt{a}[/tex].
ii) [tex]( \sqrt{a} )^2=a[/tex], for non negative values of a.
Thus,
[tex]( \sqrt{9} )^2= \boxed {1}[/tex] in simplest form. (By rule (ii))
By the Power of the Power Rule, [tex](9^{\frac{1}{2}})^2=9^{\frac{2}{2}}[/tex].
So [tex]9^{\frac{1}{2}[/tex] must equal [tex]\boxed{ \sqrt{9} }[/tex] in radical form. (This is by rule (i).)
