Power of a decreasing sequence of positive reals.

Question

If $\{a_n\}$ is a decreasing sequence of positive real numbers, then what can we say about its power $p$ where $p$ is a positive real $>1$, i.e. whether $\{a_n^p\}$ is decreasing or not?

According to me it is but how to prove it?

Answer 1

This has nothing really do do with sequences. For $p > 1$ the function $f(x) = x^p$ is increasing. So $a < b$ implies $a^p < b^p$.