Answer
(a) $z=k \frac{x^{3}}{y^{2}}$
(b) $\frac{27}{4}$
Work Step by Step
(a) Since $z$ is directly proportional to the cube of $x$ and inversely proportional to the square of $y$, we have:
$z=k \frac{x^{3}}{y^{2}}$
(b) We are given that $x$ is tripled and $y$ is doubled, so we have:
$z=k \frac{(3x)^{3}}{(2y)^{2}}=k\frac{27}{4}\frac{x^{3}}{y^{2}}$
Therefore, $z$ changes by a factor of $\frac{27}{4}$.
