In a loose sense addition is repeated successorship, multiplication is repeated addition, and exponentiation is repeated multiplication. However, the latter is the only one that isn't well defined with units. With newtons you could have $$(N+N)+(N+N+N)=5N$$ $$2N+3N=5N$$ $$(2N)(3N)=6N^2$$ but there is no $$(2N)^{3N}=8^NN^{3N}$$

Is there an alternative after multiplication that would keep units in some form? Or is exponentiation the only logical step past multiplication?


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