Unfortunately what you're implying - The Law = Sin - Paul hoped his readers of Romans would absolutely avoid thinking...
Romans 7:7
7 What shall we say then? Is the law sin? God forbid. Nay, I had not known sin, but by the law: for I had not known lust, except the law had said, Thou shalt not covet.
The phrase "The power of sin" does not connect or define the law as "sin"...or imply that the law is sin's supporter, even in the slightest.
The phrase means "the sin in us, once it knows a commandment, is immediately empowered and strengthened to disobey it".
Why?
Because we have rebellious hearts. And had the person never heard the commandment they wouldn't be motivated to break it.
...and as Paul says, this PROVES the law is good and that we are carnal/sinful.
Take a child (or even an adult) and give them a rule to follow or a boundary to stay within that they never had before (i.e. "don't do this or that") and they'll instantly be triggered in heart to do that exact thing, many times right in front of you in defiance, just because you told them what not to do.
It's possible they never even dreamed of doing the opposite, but because you told them what NOT to do they are compelled to rebel.
The power or strength of their rebellion is your rule/boundary.
So is your rule or boundary wrong or bad? No, but their rebellious nature is strengthened by your rule because the heart is evil and has not been circumcised.
Again, as Paul emphatically says, "the law is good." So to suggest or infer otherwise is unscriptural.
This is why the very law that the heart rebels against must be etched on that heart, otherwise there will continue to be death. Why? Because sin (i.e. rebellion specifically against the law of Yah) brings death.
The wages of sin is death.