Time period T of a simple pendulum may depend on m, the mass of the bob, l, the length of the string and g, the acceleration due to gravity, i.e.  

$T\propto m^a{l}^b{g}^c$

What are the values of a, b and c?

The dimensions of the two sides of proportionality are 

$T=M^a L^b {\left(L{T}^{-2}\right)}^c$ 

where LT^-2 are the dimensions of g. 

$\therefore T=M^a L^b L^c T^{-2c}=M^a L^{b+c} T^{-2c}$

 Equating the powers of dimensions on both sides, we have a = 0, b + c = 0 and - 2c = 1 

which give c =$-\frac{1}{2}$ b = $\frac{1}{2}$ and a = 0.