For which values of $a$ ($a > 0$, $a \ne 1$) is $f(x) = a^{x}$ strictly decreasing on $\mathbb{R}$?

Explanation

1. 01

   $f'(x) = a^{x}\log a$, and $a^{x} > 0$ always.

2. 02

   So $f' < 0$ exactly when $\log a < 0$, that is $0 < a < 1$.