Find the mistake in the following proof that purports to

Chapter 5, Problem 5.184

(choose chapter or problem)

Find the mistake in the following proof that purports to show that every nonnegative integer power of every nonzero real number is 1. Proof: Letr beanynonzerorealnumberandlettheproperty P(n) be the equation rn =1. Show that P(0) is true:P(0) is true becauser0 =1 by definition of zeroth power. Show that for all integers k0, if P(i) is true for all integers i from 0 through k, then P(k+1) is also true:Let k be any integer with k 0 and suppose that ri =1 for all integers i from 0 through k. This is the inductive hypothesis. We must show that rk+1 =1. Now rk+1 =rk+k(k1) becausek+k(k1) =k+kk+1=k+1 = rkrk rk1 by the laws of exponents = 11 1 by inductive hypothesis =1. Thus rk+1 =1 [as was to be shown]. [Since we have proved the basis step and the inductive step of the strong mathematical induction, we conclude that the given statement is true.]