Radical of Power of Prime Ideal

Theorem
Let $A$ be a commutative ring with unity.

Let $\mathfrak p \subseteq A$ be a prime ideal.

Let $n > 0$ be a natural number.

Then the radical of the $n$th power of $\mathfrak p$ equals $\mathfrak p$:
 * $\map {\operatorname{Rad} } {\mathfrak p^n} = \mathfrak p$