question about determinstic pushdown automata

Question

i need to show that there is no DPDA accepts the language $L=\{a^n*b^n \mid n>0\}\cup\{a^n*b^{2n} \mid n>0\}.$ i used the prefix property but i'm stuck showing that if $w,w' \in L$, $w$ is prefix of $w'$, $L$ accept $w$ and $|w|<|w'|$, why $L$ does not accept $w'$.