Hallo sigreid,
ich versuche also, noch einige Zwischenschritte zu schreiben.
Eigentlich möchte ich heureka bitten, das zu tun. Er hat eine prima Technik für solche Sachen !!
$${\left({\frac{{\mathtt{3}}}{{\mathtt{4}}}}{\mathtt{\,\small\textbf+\,}}{{\mathtt{2}}}^{\left({\frac{{\mathtt{1}}}{{\mathtt{2}}}}\right)}\right)}^{\left({\frac{{\mathtt{1}}}{{\mathtt{3}}}}\right)}{\mathtt{\,\times\,}}{{\mathtt{3}}}^{\left({\frac{{\mathtt{2}}}{{\mathtt{3}}}}\right)} = {\frac{\left({{\mathtt{3}}}^{\left({\frac{{\mathtt{1}}}{{\mathtt{3}}}}\right)}{\mathtt{\,\times\,}}{{\mathtt{2}}}^{\left({\frac{{\mathtt{1}}}{{\mathtt{6}}}}\right)}{\mathtt{\,\times\,}}{{\mathtt{3}}}^{\left({\frac{{\mathtt{2}}}{{\mathtt{3}}}}\right)}\right)}{{{\mathtt{2}}}^{\left({\frac{{\mathtt{2}}}{{\mathtt{3}}}}\right)}}}$$
= $${{\mathtt{3}}}^{\left({\frac{{\mathtt{3}}}{{\mathtt{3}}}}\right)}{\mathtt{\,\times\,}}{{\mathtt{2}}}^{{\mathtt{\,-\,}}\left({\frac{{\mathtt{1}}}{{\mathtt{2}}}}\right)} = {\frac{{\mathtt{3}}}{{{\mathtt{2}}}^{\left({\frac{{\mathtt{1}}}{{\mathtt{2}}}}\right)}}} = {\frac{{\mathtt{3}}}{{\sqrt{{\mathtt{2}}}}}}$$
Gruß radix
! ( auch an heureka !!)