Answer
$a=0.5$, $b=-0.5$
(the result is consistent with the standard formula for the speed of sound)
Work Step by Step
$$
\begin{aligned}
& c=\left(E_v\right)^a(\rho)^b \\
& , c \doteq L T^{-1} E_V \doteq F L^{-2} \rho=F L^{-4} T^2 \\
& {\left[\frac{L}{T}\right]=\left[\frac{F^a}{L^{-2 a}}\right]\left[\frac{F^b T^{2 b}}{L^{-4 b}}\right]}
\end{aligned}
$$
compare dimensions with each otherts
$$
\begin{gathered}
a+b=0 \\
2 b=-1 \\
2 a+4 b=-1 \\
a=\frac{1}{2} \text { and } b=-\frac{1}{2} \\
c=\sqrt{\frac{E_v}{\rho}}
\end{gathered}
$$
the result is consistent with the standard formula for the speed of sound
