5^(x+2)+5^(x+1) Wie kommt man von diesem Term auf diesen: 6*5^(x+1)

5^(x+2)+5^(x+1) Wie kommt man von diesem Term auf diesen: 6*5^(x+1)  ?

$$5^{(x+2)}+5^{(x+1)}\\
=5^{(x+1+1)}+5^{(x+1)}\\
=5^{(x+1)+1}+5^{(x+1)}\\
=5^{(x+1)}5^1+5^{(x+1)}\\
=5^{(x+1)}\left( 5^1+ 1 \right)\\
=5^{(x+1)} *6 \\
=6*5^{(x+1)}$$

Hallo Anonymous,

$${{\mathtt{5}}}^{\left({\mathtt{x}}{\mathtt{\,\small\textbf+\,}}{\mathtt{2}}\right)}{\mathtt{\,\small\textbf+\,}}{{\mathtt{5}}}^{\left({\mathtt{x}}{\mathtt{\,\small\textbf+\,}}{\mathtt{1}}\right)}$$ =  $${{\mathtt{5}}}^{{\mathtt{x}}}{\mathtt{\,\times\,}}{{\mathtt{5}}}^{{\mathtt{2}}}{\mathtt{\,\small\textbf+\,}}{{\mathtt{5}}}^{{\mathtt{x}}}{\mathtt{\,\times\,}}{\mathtt{5}}$$ =  $${{\mathtt{5}}}^{{\mathtt{x}}}{\mathtt{\,\times\,}}\left({{\mathtt{5}}}^{{\mathtt{2}}}{\mathtt{\,\times\,}}{\mathtt{5}}\right)$$

=  $${{\mathtt{5}}}^{{\mathtt{x}}}{\mathtt{\,\times\,}}{\mathtt{6}}{\mathtt{\,\times\,}}{\mathtt{5}}$$ =  $${\mathtt{6}}{\mathtt{\,\times\,}}{{\mathtt{5}}}^{\left({\mathtt{x}}{\mathtt{\,\small\textbf+\,}}{\mathtt{1}}\right)}$$                        $${{\mathtt{5}}}^{{\mathtt{x}}}{\mathtt{\,\times\,}}{{\mathtt{5}}}^{{\mathtt{1}}} = {{\mathtt{5}}}^{\left({\mathtt{x}}{\mathtt{\,\small\textbf+\,}}{\mathtt{1}}\right)}$$

Potenzen mit gleicher Basis werden multipliziert, indem man ihre Exponenten addiert.

Gruß radix !