I want to find dim. $\left[\mathbb{Q}\left(\sqrt[n]{a},\zeta_{n}\right):\mathbb{Q}\right]$ for positive rational number $a$ and $n^\text{th}$ root of unity $\zeta_{n}$ with assumption $\left[\mathbb{Q}\left(\sqrt[n]{a}\right):\mathbb{Q}\right]=n$. I already know $\left[\mathbb{Q}\left(\zeta_{n}\right):\mathbb{Q}\right]=\varphi\left(n\right)$, but not $\left[\mathbb{Q}\left(\sqrt[n]{a},\zeta_{n}\right):\mathbb{Q}\left(\sqrt[n]{a}\right)\right]$ nor $\left[\mathbb{Q}\left(\sqrt[n]{a},\zeta_{n}\right):\mathbb{Q}\left(\zeta_{n}\right)\right]$.
How can find dim. $\left[\mathbb{Q}\left(\sqrt[n]{a},\zeta_{n}\right):\mathbb{Q}\right]$?