I can only imagine the amount of power you would use when the blockchain becomes huge. - this has actually nothing to do with the size of the blockchain. Computing power needed to solve the puzzle (calculate correct hash for your block) is relative to the total amount of computing power used in the network (for this particular blockchain). The goal is to maintain stable creation of blocks - for example every ~10 minutes in the Bitcoin network.
I can only imagine the amount of power you would use when the blockchain becomes huge.
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