On positive integers, $nRm$ iff $n^k=m$ for some non-zero rational $k$. Is relation $R$ anti-symmetric?

Question

$X = \mathbb{Z}^+$ and $R$ is the relation defined by $nRm$ if and only if there is a non-zero $k \in \mathbb{Q}$ for which $n^k = m$. Is this relation anti-symmetric? Explain.

I'm pretty sure it isn't, but I don't know how to justify it.

Answer 1

$4,2 \in \mathbb{Z+}$

$2 = 4^{\frac{1}{2}}$ and $ 4 = 2^{2}$

Then $2R4$ and $4R2$ but $2 \not= 4$

Then isn't anti-symmetric