Answer
(a) $e^{-ln2}=\frac{1}{2}$
(b) $e^{ln(lne^{3})}=3$
Work Step by Step
The exponential function is defined by if $e^{x}=y$ then $x =lny$.
(a) $e^{-ln2}=\frac{1}{2}$
(b) Let $lnz=e^{ln(lne^{3})}$
$z=ln(e^{3}) = 3lne$
$=3$
Hence,
$e^{ln(lne^{3})}=3$