How can I equal all the numbers to zero??? Is the method given in image right or wrong??

see in the theorem when base is same power is also same has some exceptions and 1 is one of them.Other than it 0,-1 are also the exceptions .In class 6 or 7 maths book ch exponents it is mentioned the -1,1,0 are exception so in these case you cant equate power even thought base is same.