Question

If x^a=y,y^b=z,z^c=x then prove that abc=1

Answer 1

x^a=y implies x= y^1/a-----(1)

y^b= z implies y = z^1/b--(2)

z ^c = y^1/a from(1)

=(z^1/b)^1/a from (2)

z ^c= z^1/ab

therefore
c =1/ab since if a^m = a ^n then m = n

abc =1