Challenger

$a=c^2$ 

$a=c^2=(b^y)^2=b^{2y} ; c = b^y$

$\because{b=a^x} \implies{a}={b^{2y}=(a^x)^{2y}}\implies{a=a^{x2y}=a^{2xy}}$

$a=a^{2xy}$

$2xy=1$

$xy=1/2$