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Time period has the dimensions of T since it is the time taken to complete one cycle of the swinging motion. The dimensions of acceleration due to gravity are L(T^-2) , and of length are L. Now we have time period is proportional to g^a, L^b.
This gives us, 1(the dimension of time in LHS) = -2a + b (the dimension of time in RHS)
also, 0 = a + b. (from dimensions of Length in LHS and RHS). So, if one were to combine the equations, we would get a and b to be -1/2, 1/2 or that time period is equal to some constant times (L/g)^1/2.
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