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Dimensional Analysis Assistance

Hi, I've been pondering the below question and struggling. I'm relatively new to dimensional analysis and would very much appreciate some pointers.
Query:-
Use dimensional analysis to predict how the speed of sound (u) in a gas may be influenced by the gas pressure (p), gas density (r) and acceleration due to gravity (g).

My thought process so far is as follows:-
Looking at the original problem I can see we have
u=LT^-1
g=ML^-2
r=ML-3
p=ML^-1T^-2

So writing the relation with assumed powers and arbritary constant
u=K p^a r^b g^c

Taking these to be proportional and subbing in dimensions I get
LT^-1 = [ML^-1T^-2]^a [ML^-3]^b [ML-2]^c

LT^-1= M^a+b+c L^-a-3b-2c T^-2a

So working out a, b c

A+b+c = 0
-a-3b-2c = 1
-2a = - 1
a=1/2

But I come unstuck here, am I on the right track or am I barking up the wrong tree entirely?

Thanks
Edit, just seen the sticky and noticed I'm on the wrong forum.
Apologies will repost correctly!

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