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 correct answer is power.
In an expression like b^x, b is called the base, x is most commonly called the exponent but sometimes called the index (actually power is also commonly used, but erroneously), and the overall result is called the power.
One can say, "the 5th power of 2 is 32." What is 32 then? It is a power, specifically the fifth power of 2. We talk about powers of 2 (or other bases), such as 1, 2, 4, 8, 16, ... Note that 3 is not a power of 2, so if one sees 2^3, 3 should not be thought of as a power. Unfortunately, people get sloppy in their verbal expressions and might refer to "2 to the 5th power," rather than "the 5th power of 2," and they tend to think of "5th" by itself as modifying "power" so that 5 is the power, whereas they should think of all of "2 to the 5th" as what is modifying "power".
This potential backwardness is not unique to powers but applies also to division. We can say "3 divides 12 four times" or "12 divided by 3 is 4"; in the former case the divisor is stated first whereas in the latter case the dividend is stated first.
The bottom line is that we do not need to have power serve as a synonym for two already existing terms (exponent and index), while we are needing to have a name for the result of the operation.
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 $16$".
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.