This paper presents characterizations of the power distribution with the parameter $eta=1$ by the independence of the lower record values. We prove $X;{in};POW({alpha},;1)$ for ${alpha};>;0$, if and only if $frac{X_{L(n)}}{X_{L(m)}}$ and $X_{L(m)}$ for $1;{leq};m;<;n$ are independent. And we prove that $X;{in};POW({alpha},;1)$ for ${alpha};>;0$, if and only if $frac{X_{L(m)}-X_{L(m+1)}}{X_{L(m)}}$ and $X_{L(m)$ for $m;{geq};1$ are independent or $frac{X_{L(m)}-X_{L(m+1)}}{X_{L(m+1)}}$ and $X_{L(m)}$ for $m;{geq};1$ are independent.