Suppose I have a Pedersen Commitment $cm(x,r) = g^xh^r$ where $g,h$ are generators of group $G$ of prime order $p$. Based on $cm$, I want to create a commitment $cm' = (10\cdot x,r')$, without of course opening the original commitment, while knowing that $x$ is a relatively small value (e.g. less than 1 million) through a range proof.
Based on the additive homomorphic property, I was thinking of just multiplying $cm$ by itself 10 times, i.e. computing $cm^{10}$ which would open with $(10\cdot x, 10\cdot r)$. Is there anything that can go wrong with this?