# What is the name of the answer to exponentiation?

What is the name of the answer to exponentiation? Adding two numbers produces a sum. Multiplying two numbers produces a product, but I cannot think of or find the name for the solution to exponentiation.

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The sum of two numbers is not a product. As for your question, result of an exponentiation is EXPONENT. –  Kaster May 16 at 23:49
The sum is a sum –  user137794 May 16 at 23:49
Sorry, typographical error. –  Ethan May 16 at 23:55

According to Wikipedia, the result can be called a power or a product.

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Neither of these make any sense to me. I thought the power was the exponent. Also, if exponents result in a product, then can't you call the result of multiplication a sum? –  Ethan May 16 at 23:57
Both the exponent and the result can be called a power. You can consider multiplication to be the process of repeated addition, so that the result may as well be called a sum. But I don't like that either since it doesn't really hold for $5\times0.7$. I'd just go with power. –  user137794 May 17 at 0:35

The result of exponentiation is called an the $y$th power of $x$. As an example, one would say, "The $4$th power of $2$ is $16$".

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Note that unlike the case of addition and multiplication, the binary operation of exponentiation is not symmetric in its arguments. There can't be just one word denoting the result of applying exponentiation to a pair of numbers.

For example, if I gave ou the problem of applying the exponentiation operation to the pair of numbers $2$ and $3$ and that was all the information I provided you, you'd have no way of knowing whether I meant $2^3=8$ or $3^2=9$. The reason words like "sum" and "product" exist is because of the commutative properties of addition and multiplication. If addition and multiplication weren't commutative, we'd just say $a$ plus $b$ or $b$ plus $a$ and the like to refer to the result of the operation and leave it at that. But since no matter what order you add numbers you always the same value, it makes sense to create a term referring to that value, e.g., 'sum'. Exponentiation just isn't analogous to addition and multiplication in this respect.

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I believe this is not the case. We have words for difference and quotient, although subtraction and division are not commutative operations. –  GOTO 0 Dec 18 at 7:50