So I'm going through a course reviewing "fundamental" math before "advancing" to learn some new stuff. Here are some fun things I've bumped into so far.

X^{0}=1.

Whaaaaat? Yeah. Chew on that for a second. Just like the number 3 is really "positive three" and the positive is implied without being written, 3X^{3}is actually 3 * X * X *X, which is to say that X to the power of 3 represents three instances ofX with a multiplicative relationshipto the 3 or "*X". If you just write X^{3}then there's an implied 1, followed by three instances of "* X" or 1* X* X* X. So X^{0}is really 1 followed by ZERO instances of "* X", leaving you with just a lonely, invisible, implied 1. Yes, contrary to that old song that's now stuck in your head, one is not the lonliest number. X^{0}is the loneliest number.

Also, could you calculate 9^{1/2}?

I went through a whole section about the rules of exponents. Went just fine, except for me confusing myself fucking up reading the SUPER TINY SUPERSCRIPT EQUATIONS, but that was my own fault. Once I fixed my type-o's and misreads it worked out. But then the next section was square roots / radicals, and it started right off with √9 = 3 = 9^{1/2}. But how TF do I even do that? Doesn't say... In all my coursework and all the tutorials I google, bitches just say "of course we know the square root of this easy ass problem is this number..." and move on. There was nothing about fractional exponents in the exponents section.

Went to r/askmath and clicked around. Found someone with a much more advanced issue, but in their question example they did one of these. The way you calculate fractional exponents is to do the power of the numerator, so 9^{1/2}step one would be 9*1 = 9, then you root it to the degree of the denominator so^{2}√9 (which is just √9, all blank square roots are actually an implied^{2}√). Which is why the section on roots/radicals started with the explanation that √9 = 3 = 9^{1/2}. It didn't say so explicitly, but you need roots to calculate fractional exponents.