Zeige 10^(1/4)*5^(-1/4)*8^(1/4)=2 danke!!

10^(1/4) = 2^(1/4)*5^(1/4)     ;     8^(1/4) = (2^3)^(1/4)  ;   5^(1/4)*5^(-1/4)= 1

2^(1/4)*1*(2^3)^1/4=(2^4)^(1/4) = 2

$${\left({{\mathtt{2}}}^{{\mathtt{4}}}\right)}^{\left({\frac{{\mathtt{1}}}{{\mathtt{4}}}}\right)} = {\mathtt{2}}$$

Gruß radix  !

$${\sqrt[{{\mathtt{{\mathtt{4}}}}}]{{\mathtt{10}}}} = {\sqrt[{{\mathtt{{\mathtt{4}}}}}]{{\mathtt{2}}}}{\mathtt{\,\times\,}}{\sqrt[{{\mathtt{{\mathtt{4}}}}}]{{\mathtt{5}}}}$$

$${\sqrt[{{\mathtt{{\mathtt{4}}}}}]{{\mathtt{5}}}}{\mathtt{\,\times\,}}{\sqrt[{{\mathtt{-{\mathtt{4}}}}}]{{\mathtt{5}}}} = {\mathtt{1}}$$

$${\sqrt[{{\mathtt{{\mathtt{4}}}}}]{{\mathtt{8}}}} = {\sqrt[{{\mathtt{{\mathtt{4}}}}}]{\left({{\mathtt{2}}}^{{\mathtt{3}}}\right)}}$$

$${\sqrt[{{\mathtt{{\mathtt{4}}}}}]{{\mathtt{2}}}}{\mathtt{\,\times\,}}{\sqrt[{{\mathtt{{\mathtt{4}}}}}]{\left({{\mathtt{2}}}^{{\mathtt{3}}}\right)}} = {\mathtt{2}}$$

Gruß radix  !

Ich habe es Schritt für Schritt umgewandelt: