UKMT Pink Kangaroo, 2023

We will call a two-digit number power-less if neither of its digits can be written as an integer to a power greater than $1$. For example, $53$ is power-less, but $54$ is not power-less since $4 = 2^2$. Which of the following is a common divisor of the smallest and the largest power-less numbers?

(A) $3$ (B) $5$ (C) $7$ (D) $11$ (E) $13$