The lecturer has not taught us proofs yet, so I think the question is not looking for a rigorous proof. My attempt:
$$30 = 2 \times 3 \times 5$$ $$\frac{30^n}{14} = \frac{2^n \times 3^n \times 5^n}{2 \times 7} = \frac{2^{n-1} \times 3^n \times 5^n}{7}$$
Now I have written this in prime numbers, which I presume will make it easier to solve.
I feel that $7$ is not going to divide any power of $2$, $3$, or $5$.
This is as close as I can get to a proof.