induction - Discrete Math problem

I believe this is an induction problem.

Let $a, b$ be positive integers with $a < b$. Prove that for any natural number $n$, $a^n < b^n$.

I feel I should start with a base case $n = 1$ which yields true since $a$ is already less than $b$.

Next I would implement the induction hypothesis, but I'm kinda shaky on what that is.

After that I would check the $n + 1$ case.

Could someone check and verify what I'm doing?

Answer

For $n\in\Bbb Z^+$ let $P(n)$ be the statement that $a^n