For this problem, we are told that two variables, x, and y, vary inversely. We need to determine which expression represents the relation for a pair of values.
When two variables vary inversely, we can write their relation as:
[tex]xy=k[/tex]
Replacing the values, we have:
[tex]\begin{gathered} a\cdot a^2=k\\ \\ k=a^3 \end{gathered}[/tex]
Therefore the expression is:
[tex]\begin{gathered} xy=a^3\\ \\ y=\frac{a^3}{x} \end{gathered}[/tex]
The correct option is C.
