mathematics - How to read exponential expressions, e.g., "2^16"?

How do you say the mathematical function in English:

x^y (or x^y)

For example, how do you say

2^16 (or 2¹⁶)

I know ^ means 'power' or 'exponentiate', but that is the name of the operation, not how you pronounce its use.

If y = 2, it is 'x squared', y=3 then 'x cubed'. What if y is some other arbitrary number?

Answer

The references say "two to the sixteenth power" or "two to the power of sixteen" but that is only done in very formal speech. Ironically, in actual mathematical usage, the formal pronunciation is not that common.

The more common way to say it (in math class or in a mathematical presentation) is a ellipsis of the first:

two to the sixteenth

or just as commonly

two to the sixteen

depending on how rapid speech you are using.

Of course there are some special cases: x² is "x squared", x³ is "x cubed". x¹ or x⁰ are mathematically jarring if written alone (they are often, when mathematically allowed, written just "x" and "one"), but if forced would be "x to the one" and "x to the zero", never as an ordinal (it is a solecism to say "x to the first" and way too informal to say .

For example, a polynomial x¹⁰⁹ + 9x⁵ − 2x² is most likely pronounced:

x to the hundred and nine plus nine x to the fifth minus two x squared.

(or "hundred and ninth"; both are equally possible here). If it were x¹⁰¹ — see discussion here —, you just don't say "one hundred first".)

If variables are involved, the ordinal is not used. x^y is

x to the y

(that is, not appending the ordinal suffix '-th').