Answer
$\color{blue}{z=\frac{1}{17}(x^3+y^2)}$
Work Step by Step
RECALL:
(1) If $y$ varies directly as $x$, then $y=kx$ where $k$ is the constant of proportionality.
(2) If $y$ varies inversely as $x$, then $y=\dfrac{k}{x}$ where $k$ is the constant of proportionality.
Notice that when the variation is direct, the variable is on the numerator while if the variation is inverse, the variable is in the denominator.
$z$ varies directly with the sum of the cube of $x$ and the square of $y$. Thus, the equation of the variation is:
$z=k(x^3+y^2)$
Since $z=1$ when $x=2$ and $y=3$, substituting these into the tentative equation above gives:
$\require{cancel}
z=k(2^3+3^2)
\\1=k(8+9)
\\1=k(17)
\\\frac{1}{17}=\frac{k(17)}{17}
\\\frac{1}{17}=k$
Thus, the equation of the inverse variation is:
$\color{blue}{z=\frac{1}{17}(x^3+y^2)}$
