Question

Let x_n = (a^n+b^n)^(1/n), where 0 < a < b. Use the squeeze theorem to show that the limit of x_n as n approaches inf is b.
What I know:
b^n \le a^n+b^n \le 2b^n (where \le is less than or equal to)
b^n >>> a^n as n tends to inf
b^(1/n) tends to 1 as n tends to inf