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,

"rewrite with positive exponents, and simplify; if possible"
Here is the specific problem itself,



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

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.