My assignment this semester is to help out in a Math Lab. (That's MATH, not METH!) Since our clientele has been virtually non-existent during first block, the teacher thought I may be able to drum up business if I hung out in the student cafeteria, where students would be for second arrival and second breakfast. Well, yesterday a bunch of students sat at the other end of the table I staked out. And this morning, one of them said, "You're the Math Lady, right?" (the little title on the sign I drew up to hang on the crate in front of me - it's not as pretentious as the other title the teacher suggested, the Math GODDESS!) I answered in the affirmative. She scooted over with a pile of papers and asked helped in solving multi-step equations with variables on both sides. For instance:
3X + 2(x-3) = 5X - 6
Simple algebra. I helped her remember about her distributive property and watching out for negative signs, and getting all her variables on one side, and about adding negatives. Her friend, seeing the progress, pulled out some of her own papers. But hers were entirely different, dealing with radicals and exponents, and RATIONAL exponents. If you're like me when my mathematically brilliant son talks to me about the "number e", you are probably imitating the teacher on the Peanuts cartoons -
I made a note of what she was facing, and apologized to her, saying I'd been out of touch with Math all last year and had to do some review. I helped her with a couple of simpler ones, and assured her I'd be there Monday as well.
So when I got up to the classroom, I hauled out the two-ton Algebra textbook and looked in the index and turned to the chapter dealing with these mathematical monstronsities. Of course they had some simple examples, and I leanred how to work the graphing calculator to work them out : Given a number to a fraction of a power, you hit the number, then the carat ^ then top number, divide by, bottom number, enter. Okay. But what about THIS one:
(5X) to the negative 5 over 4 power? Well, you change it to the 4th root of 5X, to the negative 5th power, but of course, they don't like you putting a NEGATIVE exponent, so you have to transpose it, put that all under a one,to make it a positive exponent. BUT WAIT! You can't leave it THAT way because the Math Gods don't like radical signs in the denominator! Now, if it was simply a square root, it would be easier, but this is a 4th root, to the FIFTH POWER.
Am I losing you yet?
Yeah, that's what I THOUGHT!