The expression $n = p_1^{e_1}\cdot p_2^{e_2}\cdots p_k^{e_k}$ represents the prime factorization of the number $n$. The numbers $p_i$ are distinct prime numbers, and the numbers $e_i$ are the exponents for each of the prime numbers in the factorization. 

• Say $n = 72$, so its prime factorization is  $n = 2^3 \times 3^2$. Since there are three $2$'s and two $3$'s in the prime factorization of $72$, it is not possible to split them in two equal groups, the closest would be $(2^2 \times 3) \times (2 \times 3)$, so $72$ is not a perfect square.
• Say $n = 36$, so its prime factorization is $n = 2^2 \times 3^2$. This time it is possible to do $n = (2 \times 3) \times (2 \times 3)$, since we have an even number of each factor. So $\sqrt{n} = 2 \times 3$. (Note both $n$ and $\sqrt{n}$ have the same prime factors, and exponents of the prime factorization of $\sqrt{n}$ are exactly half of the exponents of $n$.)