Option A: $a$
By Theorem 1.2, if $p$ is a prime and $p$ divides $a^2$, then $p$ divides $a$, where $a$ is a positive integer.
Source: Chapter 1, Section 1.3 (Theorem 1.2)
This is a direct application of Theorem 1.2 from the textbook. The theorem states specifically that if a prime $p$ divides $a^2$, it must divide $a$ itself (not any fractional power of $a$). The other options involve fractional indices which are not integers, so the theorem does not apply to them. For MCQs like this, simply recall the exact theorem statement.