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a) What combination of ratios and/or products of C, H, and M sub p will yield a new quantity of dimensions (L)?

b) What combination of ratios and/or products of C, H, and M sub p will yield a new quantity of dimensions (T)?

I have no idea how to figure this out. I am brand new to physics so any help would be greatly appreciated. Could you please solve the question and walk me through how you found the answer? I am a very literal learner and I need to see the answer along with how you found it.

This is what I came up with, not sure if it's correct:

(C^a)*(H^b)*(M^c)

L^(a+2b)=L----> a+2b=1

M^(b+c)= 1-----> b+c=0

T^(a-b)=1---->a-b=0

a=-b

b=1

a=-1

c=-1

(C^-1)*(H^1)*(M^-1)=H/C*M

-a-b=1

a+2b=0

b+c=0

b=1

a=-2

c=-1

So, H/M*c*c

part A= H/M*C

part B= H/M*C*C