In two of the Hugo Award-nominated works of fiction, equations appear in the text.
In one of them, a power of a variable is represented with ^, a caret. In the other, multiplication is represented with *, an asterisk.
Both of those notations are very common in plain-ASCII-text email. But it seems unlikely to me that a professional mathematician would use either, especially in a setting other than modern-day Earth.
Raising a number to a power has traditionally been represented by a superscript. Multiplication has traditionally been represented by putting terms next to each other, or by ·, a dot (placed higher than where a period goes), or sometimes by ×, an x-shaped multiplication sign.
Why am I writing about this here? This isn’t a math blog! But symbols and notation are within this blog’s purview, and that’s what I’m focused on here.
If a book were written in ASCII text, then using notation like carets and asterisks might be the best we could do to represent powers and multiplication. But these days, even books that aren’t written with specialist typesetting can include some mathematical notation by using Unicode, which lets you represent a far broader range of characters than a traditional American typewriter keyboard provides. And superscripts have been part of publishing for a very long time.
I should note that there are plenty of mathematical things that Unicode can’t do; for example, although there are Unicode characters for some common fractions like ½, there’s no really good way in Unicode to represent an unusual fraction like 79/91, nor to show division as part of an equation, nor to show square roots. For aspects of math notation that Unicode can’t handle, you need more specialized typesetting. On web pages and maybe in some ebooks, you can use MathML, a.k.a. Mathematical Markup Language, but for printed books, you presumably need to use other software that lets you lay out equations.
But even so: If you’re a writer, an editor, or a publisher, then next time you want to include an equation in your text, take a moment to consider whether the notation that you’re using is a simplified plain-text version of standard professional math notation, and consider using notation that’s more in keeping with what a mathematician would use.