Units of three physical quantities X,Y and Z are g. `cm^(2) .s ^(-5), g. s^(-1)` and cm .`s^(-1)` . Find the relationship between X,Y and Z.

Explanation

Let X = k`Y^(a)Z^(b)` , where k is a dimensionless constant a and b are numeric indices. From given units dimension of X = `ML^(2)T^(-5)` those of Y and Z are `MT^(-1)` and `LT_(-2)` respectively.
`:." "ML^(2)T^(-5)=(MT^(-1))^(a)(LT^(-2))^(b)`
`=M^(a)L^(b)T^(-a-2b)`
Equating powers of the same base
a = 1, b = 2
`:." " X = kYZ^(2)`.