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There really is no direct relation between Steem Power and Reputation. 

SteemPower is just the stake you have on Steem. The more stake you have, the more your votes and your account will be worth. Reputation on the other hand is "supposed" to be a visual indicator to see who are the trustworthy one's on this platform and who are the veterans. If you might have noticed, everytime someone upvotes your post your Reputation increases. The more upvotes you get the more high your reputation is.

Having said that, someone actually made a post showing how Reputation is directly linked to the number of received upvotes. In this post https://steemit.com/steemit/@holger80/reputation-can-be-directly-linked-to-the-amount-of-received-upvotes it is seen that the more high the reputation of an account is, the more upvotes he have already received and thus the more Steem and SP he had accumulated.

If we assume that an account never powers down then we can say that there really is somewhat a relation between Steem Power and Reputation. A higher rep account is most likely to have a big Steem Power.

There is no relationship between steempower and reputation

Steempower is essentially how much you have invested or vested in Steem. This determines how much your vote is worth.

Reputation is a score heavily based on how many upvotes you have received over all. This allows someone to simply "buy" their reputation score.

Based on your response , how can anyone " buy" a reputation score since it is based on upvoted?

By using upvote bots

Yes of course. Noted!!

Talking about the relationship between steempower and reputation is of course closely related. Because steempower and reputation shows that someone is active in steemit. But if you speak which is more influential. Of course steempower.

reputation score can be said as a number that shows the activeness of a steemians in making original and interesting posts in steemit.

and it can also be said that the higher the reputation score of an account, meaning the more knowledge of the world of steemit it has. While Steem Power is one that shows the upvote power of each account.

Absolutely none. 

The reality is that our reputation increases the moment we received "Upvotes" from users. That's the basic fact. The upvote value that we receive pertain a certain amount of Steempower - so as our reputation.

The bigger Steem Power holders upvoting as (and considering the voting weight placed), the bigger boost on reputation received. The computation for determining one's reputation is the accumulation of Vests a user received from the votes.

With the accumulation of Vests (Steem Power) from the votes received, a users reputation increases. The same thing it will happen with downvoting, a user's reputation will decrease when users downvote his posts (Steem Power and voting weight will still matter).