Hey my name's Jeff, nice to meet you all! would appreciate some help.

Hi! My name is Jeff, I'm interested in mathematics, physics, life science/chemistry as well as computer science. I plan to transfer to a 4-year university to attain a bachelors in science. I just finished up my first semester at college and it seems to be going well and I'm here to get better at mathematics. Nice to meet you all I hope to make friends here and really improve upon skills. :) With that said I'd really appreciate some help understanding index roots, even and odd kth roots, etc "nth roots" and clear up a lot of confusion I'm having.

My algebra text book talks about kth roots, even and odd ones I was wondering if nth roots are generally meant to mean the same thing?

Is it a wise idea to memorize a table of common cube roots and square roots in order to get faster/better at doing these types of problems? Such as "taking roots".

My textbook says,

Quote:

"rewrite with positive exponents, and simplify; if possible"

Here is the specific problem itself,

16^{-1/4 }

then,

$\displaystyle \frac{1}{\sqrt[4]{16}}$

I basically just put 1 on top of a rational expression to make up for taking -1 away; and then represented 16 as a square root with an index of 4.

now this is as far as I went to answer the question, but in my text book it says that the answer is 1/2? Can someone explain to me why and how?? My best guess is that since it is an even index, with no negatives involved whatsoever that it is just N? and n is 2? and then just put 1 over 2 and represent it as a fraction? I'm completely utterly lost in the time it took me to learn the LaTeX required to type this out, lol ; 2 x 2 is 4 x 2 is 8 x 2 is 16. so what I'm taking 2 out of this logic? ; I don't wanna settle for the crappy explanation the textbook gave me and my teacher just blasted through this subject. I really want to understand in as great detail as possible.

You know , in general , I know I couldn't say a lot it's just I'm so use to doing math on paper this thing wants me to translate it using a programming language of some sort, LaTeX? I guess I'll learn that along the way then lol.