Are coefficients in a reaction taken as the exponents in the rate law expression?
But when i researched on rate of expression i undertood that a, b and c are not coefficients of the reaction


You are correct. $a,b$ and $c$ summed together represent the order of the reaction. Note that this is very different from the molecularity of a reaction.


  But in most part of my book the coefficients are taken as the powers a b and c 


Without knowing the reactions for which this is done, it is impossible to comment further. However, assuming that the book is correct, we can say, that in those specific cases, your book was dealing with elementary reactions.

Recall that molecularity of an elementary reaction is the same as its order. However, most natural reactions occur through complex mechanisms, and in those cases, molecularity is rarely equal to its order.

For more details on the difference between molecularity and order of a reaction, have a look at this question.