Field elements which become $n$th powers after adjoining an $n$th root of unity

$-4=(1+i)^4$ became a fourth power when $i$, a primitive fourth root of unity, was adjoined to $\Bbb{Q}$.

Take $K=\mathbb R$ and $L=\mathbb C=K(i)$. Then all elements of $K$ become fourth powers in $L$. Note that $i$ is a primitive fourth root of unity. Only the positive real numbers are already fourth powers in $K$.