#### Answer

(a) $z=kx^{3}y^{5}$
(b) 864

#### Work Step by Step

(a) Since $z$ is jointly proportional to the cube of $x$ and the fifth power of $y$, we have:
$z=kx^{3}y^{5}$
(b) We know that $x$ is tripled and $y$ is doubled, so we have:
$z=k(3x)^{3}(2y)^{5}=864kx^{3}y^{5}$
Therefore, $z$ changes by a factor of $864$.