Precalculus, Chapter 9, 9.4, Section 9.4, Problem 28

You need to use mathematical induction to prove the inequality, hence, you need to perform the following two steps, such that:
Step 1: Basis: Prove that the statement holds for n = 1
If xStep 2: Inductive step: Show that if P(k) holds, then also P(k + 1) holds.
P(k): (x/y)^(k+1) <= (x/y)^k holds
P(k+1): (x/y)^(k+2) <= (x/y)^(k+1)
(x/y)^(k+1)*(x/y) <= (x/y)^(k+1) => x/y <= 1 => x <= y true
Hence, since both the basis and the inductive step hold, the statement P(n): (x/y)^(n+1) <= (x/y)^n holds for all indicated values of n.