In [1]:

```
import proveit
theory = proveit.Theory() # the theorem's theory
```

In [2]:

```
%proving exp_rational_non_zero__not_zero
```

Proof by contradiction. Assume $a^b = 0$. Since $(a^b)^{1/b} = a$ and $0^{1/b} = 0$ then $a = 0$. But that contradicts our restriction on $a$ to be in $\mathbb{Q}^{\neq 0}$.