A number $v = xy$ with an even number $n$ of digits formed by multiplying a pair of $n/2$-digit numbers (where the digits are taken from the original number in any order) $x$ and $y$ together. Pairs of trailing zeros are not allowed. If $v$ is a vampire number, then $x$ and $y$ are called its "fangs."
Quoted from http://mathworld.wolfram.com/VampireNumber.html
Example: $60 \cdot 21 = 1260$
Does there exist a non-trivial vampire number $v $ such that
$v = xy = a^bb^a$ with integers $ a,b > 1 $ ?
Is there a way to show that this $v$ exists without having to check every known vampire number with an algorithm?