+20 i have a $${\sqrt{{\mathtt{a}}}}$$ and the same as $${{\mathtt{a}}}^{\left({\frac{{\mathtt{1}}}{{\mathtt{2}}}}\right)}$$;
then it is equal to $${{\mathtt{a}}}^{\left({\mathtt{1}}{\mathtt{\,\times\,}}\left({\frac{{\mathtt{1}}}{{\mathtt{2}}}}\right)\right)}$$;
according to the identities ($${{\left({{\mathtt{a}}}^{{\mathtt{n}}}\right)}}^{{\mathtt{k}}} = {{\mathtt{a}}}^{\left({{\mathtt{n}}}^{{\mathtt{k}}}\right)} = {{\mathtt{a}}}^{\left({\mathtt{n}}{\mathtt{\,\times\,}}{\mathtt{k}}\right)}$$) it is the same as $${{\mathtt{a}}}^{\left({{\mathtt{1}}}^{\left({\frac{{\mathtt{1}}}{{\mathtt{2}}}}\right)}\right)}$$;
in this case it is the same as $${{\mathtt{a}}}^{{\sqrt{{\mathtt{1}}}}} = {{\mathtt{a}}}^{{\mathtt{1}}}$$;
$${{\mathtt{a}}}^{{\mathtt{1}}} = {\mathtt{a}}$$;
SO: I have proven a false statement $${\mathtt{a}} = {\sqrt{{\mathtt{a}}}}$$;
could you help me understand the problem?
