Help! Exponents are too hard for me

[Aliza]

Sorry again this sounded patronizing.  I was just trying to (humorously) err on the side of comprehensibility.

Your explanation is beautiful and I mean that from the bottom of my heart. If you and I ever get to talking off the forum and I mention what my background is, you’ll know that I said that with absolute sincerity. If I had seen that explanation from the start, I’d have understood immediately. I needed it to be put in context of something that made more sense to me. Of course you can’t change the base of an exponent.

I’ve never done math induction and, for example, we were told to disregard the leading portion of the LHS in our answer, so in my answer, I’m writing something like “….+blah, blah = 2(blah, blah) to the k+1”. I didn’t understand that the LHS isn’t supposed to equal the RHS, but rather that the whole expression is supposed to prove that the equation is true in different cases of k. At first, all I saw was that the LHS didn’t equal the RHS, and my Aliza-brain saw this as breaking the rules of math, and therefore, it must be that no math rules apply. –I have since been sorted out.

I’m in this class where I’m seeing stuff from pretty much every math class I’ve taken to date, and some stuff from classes I’ve craftily avoided. I’m pushing my brain to learn new stuff on the fly and try to remember stuff I haven’t touched in a long time. Plot the complex number in the complex plane and write it in polar form. Lol! Easy! Find the complex conjugate of 6-4i? I knew it had something to do with a sign change, but I expected a little more complexity to the question given that it was sandwiched between two other questions from back in Calc 2. (punchline for casual browsers: it’s 6+4i). ... maybe that's the whole point my professor is trying to drive in. Just look at the question and answer it for what it is rather than approaching it with some expectation.

I just want to say again, Reltzik. I really appreciate your reply. It was very professional and sensitive.