整理a^b^/a^4-2b^4=1,得,
a²b²=a^4-2b^4
a^4-a²b²-2b^4=0,
a^4+a^2b^2-2a^2b^2-2b^4=0,
(a^4+a^2b^2)-(2a^2b^2+2b^4)=0,
a^2(a²+b^2)-2b^2(a^2+b^2)=0
(a^2+b^2)(a^2-2b^2)=0,
所以a^2+b^2=0,或a^2-2b^2=0,
当a^2+b^2=0时,a=b=0,
此时条件式子的分母a^4-2b^4为0,没有意义
当a^2=2b^2时,
(a^-b^)/(2a^+3b^)
=b^2/7b^2
=1/7
选D