# Degree of field extention $\mathbb{F}_{p^q} / \mathbb{F}_p$

Let $p, q$ be prime numbers.

What is the degree of field extension of $\mathbb{F}_{p\ ^q} / \mathbb{F}_p$

I have no idea on this but if I had to guess I would say $q$ ?

Any help or insight is deeply appreciated.

• Iteratively construct a basis to show that $\mathbb{F}_{p^q}$ is a $q$-dimensional $\mathbb{F}_p$-vector space. – reuns Sep 7 '17 at 5:05
• How many elements are there in an $n$-dimensional vector space over $\Bbb{F}_p$? – Jyrki Lahtonen Sep 7 '17 at 5:55