Answer
(a) $z= \frac{k}{x^{2}y^{3}}$
(b) $\frac{1}{72}$
Work Step by Step
(a) Since $z$ is inversely proportional to the square of $x$ and the cube of $y$, we have:
$z= \frac{k}{x^{2}y^{3}}$
(b) We know that $x$ is tripled and $y$ is doubled, so we have:
$z= \frac{k}{(3x)^{2}(2y)^{3}}=\frac{1}{72}\frac{k}{x^{2}y^{3}}$
Therefore, $z$ changes by a factor of $\frac{1}{72}$.
