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Plank's units are physical quantities formed as suitable combinations of light $c = 3.00 .10^8 ms^-1$. Reduced plank's constant is $h = 1.05 .10^-34 kgm^2 s^-2$ and gravitational constant $G = 6.67.10^-11 kgm^3s^-2$. That means we may write $A = c^a . h^b. G^c$ (a, b, c are numbers) obtaining all sorts of physical quantities A. Consider such an expression for linear mass density, which is usually denoted by $\lambda$ and has units $kg.m^-1$. What is the value of plank's linear mass density?

This problem appeared in my Regional Physics Olympiad 2021. I was failed to solve this one. But, I don't want to make mistakes anymore in my National Contest. Requiring your help regarding this Problem.

here is the solution(maybe do check the calculation)

Great. Thanks a lot for your approach. But the problem is I am facing difficulty in order to find the actual answer. It would so kind of you if you help me regarding plugging the values and find the actual answer. Please help me because after 2 days I have to attend the contest.