$${\frac{\left({{\mathtt{2}}}^{{\mathtt{199}}}{\mathtt{\,-\,}}{{\mathtt{2}}}^{{\mathtt{198}}}\right)}{\left({{\mathtt{2}}}^{{\mathtt{199}}}{\mathtt{\,\small\textbf+\,}}{{\mathtt{2}}}^{{\mathtt{198}}}\right)}} = \left({\frac{{{\mathtt{2}}}^{{\mathtt{198}}}{\mathtt{\,\times\,}}\left({\mathtt{2}}{\mathtt{\,-\,}}{\mathtt{1}}\right)}{\left({{\mathtt{2}}}^{{\mathtt{198}}}{\mathtt{\,\times\,}}\left({\mathtt{2}}{\mathtt{\,\small\textbf+\,}}{\mathtt{1}}\right)\right)}}\right)$$ = $${\frac{{\mathtt{1}}}{{\mathtt{3}}}}$$
$${{\mathtt{2}}}^{{\mathtt{199}}} = {\mathtt{2}}{\mathtt{\,\times\,}}{{\mathtt{2}}}^{{\mathtt{198}}}$$ Man kann $${{\mathtt{2}}}^{{\mathtt{198}}}$$ ausklammern und dann kürzen !
Ergebnis deiner Potenzaufgabe = 1/3 = $${\frac{{\mathtt{1}}}{{\mathtt{3}}}}$$ !
Zur Erläuterung:
$${\frac{\left({{\mathtt{a}}}^{{\mathtt{3}}}{\mathtt{\,-\,}}{{\mathtt{a}}}^{{\mathtt{2}}}\right)}{\left({{\mathtt{a}}}^{{\mathtt{3}}}{\mathtt{\,\small\textbf+\,}}{{\mathtt{a}}}^{{\mathtt{2}}}\right)}} = {\frac{{{\mathtt{a}}}^{{\mathtt{2}}}{\mathtt{\,\times\,}}\left({\mathtt{a}}{\mathtt{\,-\,}}{\mathtt{1}}\right)}{\left({{\mathtt{a}}}^{{\mathtt{2}}}{\mathtt{\,\times\,}}\left({\mathtt{a}}{\mathtt{\,\small\textbf+\,}}{\mathtt{1}}\right)\right)}}$$ = $${\frac{\left({\mathtt{a}}{\mathtt{\,-\,}}{\mathtt{1}}\right)}{\left({\mathtt{a}}{\mathtt{\,\small\textbf+\,}}{\mathtt{1}}\right)}}$$
Gruß radix 
!
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